 # Bearing and Distance

### Bearing and Distance

The bearing and distance is an example of applied knowledge of trigonometry. The navigation used on land, sea or air was done using bearing (at least before GPS was invented and widely used). In this topic, we will learn how to use the bearing to calculate the distance or position of one place to another.

We will use the convention for bearing as follows:
– three-figure or three-digit
– North or N is the reference for $${\small 0^{\large{\circ}}}$$
– measured in the clockwise direction from the North I have put together some of the questions I received in the comment section below. You can try these questions also to further your understanding on this topic.

To check your answer, you can look through the solutions that I have posted either in Youtube videos or Instagram posts.

You can subscribe, like or follow my youtube channel and IG account. I will keep updating my IG daily post, preferably.

Furthermore, you can find some examples and more practices below! =).
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QUESTIONS FROM STUDENTS:

$${\small 1.\enspace}$$ A ship is 4 km due north and then 3 km on a bearing of $${\small 60^{\large{\circ}}}$$. Find the distance from his original position.

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$${\small 2.\enspace}$$ A boat sails round a quadrangular course ABCD, starting from A to B in 4 km due east of A, C is 3 km due south of B and D is 4 km S50W from C.
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What is the distance and bearing of A from D?

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$${\small 3.\enspace}$$ $${\small\hspace{0.2em}\left(\textrm{a}\right).\hspace{0.8em}}$$ A village is 10 km on a bearing $${\small 050^{\large{\circ}}}$$ from a point O. How far is the village North of O?
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$${\small\hspace{1.6em}\left(\textrm{b}\right).\hspace{0.8em}}$$ The angle of elevation of the top of a building from a point 80 m away on a level ground is $${\small 25^{\large{\circ}}}$$.
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Calculate the height of the building to the nearest metre.

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$${\small 4.\enspace}$$ Town F is 50 km east of Town G. Town H is on a bearing of $${\small 040^{\large{\circ}}}$$ from Town F. The distance from F to H is 65 km.
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Calculate, to the nearest km, the actual distance GH.
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Calculate, to the nearest degree, the bearing of H from G.

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$${\small 5.\enspace}$$ A village R is 10 km from a point P on a bearing $${\small 025^{\large{\circ}}}$$ from P. Another village A is 6 km from P on a bearing of $${\small 016^{\large{\circ}}}$$. Calculate,
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$${\small\hspace{1.2em}\left(\textrm{a}\right).\hspace{0.8em}}$$ the distance of R from A and
$${\small\hspace{1.2em}\left(\textrm{b}\right).\hspace{0.8em}}$$ the bearing of R from A

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$${\small 6.\enspace}$$ The bearing of city R from city M is $${\small 058^{\large{\circ}}}$$ and the bearing of city K from city M is $${\small 310^{\large{\circ}}}$$.
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If the distance from M to R is 40 km and that of M to K is 70 km,
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What is the distance between K and R to 1 decimal place and bearing of K from R
to the nearest degree?

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$${\small 7.\enspace}$$ The bearing of two points Q and R from a point P are $${\small 050^{\large{\circ}}}$$ and $${\small 120^{\large{\circ}}}$$ respectively.
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If PQ = 12 cm and PR = 5 cm, find the distance QR.

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$${\small 8.\enspace}$$ A ship leaves a port at noon and has a bearing of $${\small 207^{\large{\circ}}}$$. If the ship is traveling at 20 miles per hour, how many miles south and how many miles west is the ship from its departure point at 6 pm?

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$${\small 9.\enspace}$$ From a point H at a harbour, the bearing of two ships A and B on the high sea are $${\small 160^{\large{\circ}}}$$ and $${\small 220^{\large{\circ}}}$$ respectively. B is 14 km from H and the bearing of A from B is $${\small 085^{\large{\circ}}}$$.
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$${\small\hspace{1.2em}\left(\textrm{a}\right).\hspace{0.8em}}$$ How far apart are the two ships?
$${\small\hspace{1.2em}\left(\textrm{b}\right).\hspace{0.8em}}$$ What is the bearing of B from A?

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$${\small 10.\enspace}$$ An aircraft travels 120 km on a bearing of $${\small 062^{\large{\circ}}}$$ and then 95 km on a bearing of $${\small 305^{\large{\circ}}}$$. How far is the aircraft from the starting point?

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$${\small 11.\enspace}$$ Two boats A and B left a port C at the same time on different routes. B travelled on a bearing of $${\small 150^{\large{\circ}}}$$ and A travelled on north side of B. When A had travelled 8 km and B travelled 10 km, the distance between the two boats was found to be 12 km. Calculate the bearing of A’s route from C.

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$${\small 12.\enspace}$$ An aeroplane flies from town X on a bearing of $${\small 45^{\large{\circ}}}$$E to another town Y with a distance of 200 km. It then changes course and flies to another town Z on a bearing of S$${\small 60^{\large{\circ}}}$$E. If Z is directly east of X, calculate correct to 3 s.f.:
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$${\small\hspace{1.2em}\left(\textrm{a}\right).\hspace{0.8em}}$$ the distance from X to Z.
$${\small\hspace{1.2em}\left(\textrm{b}\right).\hspace{0.8em}}$$ the distance from Y to XZ.

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$${\small 13.\enspace}$$ A,B,C are three locations on the same horizontal plane. B is on a bearing of $${\small 041^{\large{\circ}}}$$ from A and the distance is 40 km. C is directly due north of A and the distance between B and C is 35 km. Find the bearing of C from B.

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$${\small 14.\enspace}$$ The bearing of A from B is $${\small 129^{\large{\circ}}}$$ and the bearing of C from B is $${\small 219^{\large{\circ}}}$$. If B is equidistant from A and C, find the bearing of C from A.

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$${\small 14.\enspace}$$ A,B,C are three locations on the same horizontal plane. B is on a bearing of $${\small 041^{\large{\circ}}}$$ from A and the distance is 40 km. C is directly due north of A and the distance between B and C is 35 km. Find the bearing of C from B.

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$${\small 15.\enspace}$$ A ship sails 50 km north from a point A, then 25 km west and finally 50 km on a bearing of $${\small 315^{\large{\circ}}}$$.
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$${\small\hspace{1.2em}\left(\textrm{a}\right).\hspace{0.8em}}$$ How far west is the ship from the point A?
$${\small\hspace{1.2em}\left(\textrm{b}\right).\hspace{0.8em}}$$ How far north is the ship from the point A?
$${\small\hspace{1.2em}\left(\textrm{c}\right).\hspace{0.8em}}$$ Find the distance and bearing of the ship destination from A?

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EXAMPLE:

$${\small 1.\enspace}$$ A, B and C are three towns located on a horizontal ground. It is given that AC $$=$$ 22 km and BC $$=$$ 18 km. C is at a bearing of $${\small 025^{\large{\circ}}}$$ from A and $${\small 337^{\large{\circ}}}$$ from B.
$${\small\hspace{1.2em}\left(a\right).\hspace{0.8em}}$$ Show that $${\small \angle {ACB} = 48^{\large{\circ}}}$$.
$${\small\hspace{1.2em}\left(b\right).\hspace{0.8em}}$$ Calculate
$${\small\hspace{2.8em}\left(i\right).\hspace{0.7em}}$$ the distance AB,
$${\small\hspace{2.8em}\left(ii\right).\hspace{0.7em}}$$ the bearing of A from B,
$${\small\hspace{2.8em}\left(iii\right).\hspace{0.5em}}$$ the area of triangle ABC,
$${\small\hspace{2.8em}\left(iv\right).\hspace{0.7em}}$$ the shortest distance from B to AC.
$${\small\hspace{1.2em}\left(c\right).\hspace{0.8em}}$$ A helicopter, H, is hovering directly above a point D, nearest to B on AC. If the angle of elevation of H seen from B is $${\small 10^{\large{\circ}}}$$, calculate the height of H above D.
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$${\small 2.\enspace}$$ A ship leaves port at noon and has a bearing of $${\small 207^{\large{\circ}}}$$. If the ship is traveling at 20 miles per hour, how many miles south and how many miles west is the ship from its departure point at 6 pm?

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$${\small 3.\enspace}$$ From the lookout tower A, a column of smoke is sighted due south. From a second lookout tower B, 5 miles west of A, the smoke is observed with a bearing of $${\small 117^{\large{\circ}}}$$. How far is the fire from tower B? How far is it from tower A?

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$${\small 4.\enspace}$$ Pittsburgh is 117 miles due south of Kansas City. A plane leaves Kansas City at noon and flies 200 mph with a bearing of $${\small 201^{\large{\circ}}}$$. When, to the nearest minute, will the plane be due west of Pittsburgh?

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$${\small 5.\enspace}$$ Two ships A and B leave port at the same time with ship A sailing with a bearing of $${\small 023^{\large{\circ}}}$$ at the speed of 11 mph and ship B sailing with a bearing of $${\small 113^{\large{\circ}}}$$ at 15 mph. Approximate the bearing from ship B to ship A one hour later.

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PRACTICE MORE WITH THESE QUESTIONS BELOW!

$${\small 1.\enspace}$$ Two ships, A and B leave port at 13 00 hours. Ship A travels at a constant speed of 18 km per hour on a bearing of $${\small 070^{\large{\circ}}}$$. Ship B travels at a constant speed of 25 km per hour on a bearing of $${\small 152^{\large{\circ}}}$$. Calculate the distance between A and B at 15 00 hours.
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$${\small 2. \enspace}$$ A plane is 120 miles north and 85 miles east of an airport. If the pilot wants to fly directly to the airport, what bearing should be taken?

$${\small 3. \enspace}$$ Ohio is 190 miles due north of Virginia. Stamford is due east of Ohio and is 460 miles from Virginia. What is the bearing angle heading from Virginia to Stamford? What is the bearing angle from Stamford to Virginia?

$${\small 4. \enspace}$$ D is 30 km due east of A. A ship sails from A on a certain bearing for 15 km to B. It then sails to C, which is 40 km from A and due north of D. Finally it sails due south to D. AB is the bisector of $${\small \angle {EAC}}$$. Calculate the total distance for the whole journey.
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$${\small 5. \enspace}$$ An observer at a radar station plots an aircraft due north of him and at a range of 50 km, measured horizontally. The aircraft keeps on traveling due west at a constant height. The bearing of the plane from the observer 10 minutes later is $${\small 300^{\large{\circ}}}$$. Calculate the speed of the aircraft in km/h.

$${\small 6. \enspace}$$ N is north of S. NS is the tangent to the circle, radius 1 km, at T. A man walks 2 km along the circle from T to P. What is the distance and bearing of P from T?
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$${\small 7. \enspace}$$ In the diagram, A, B, C and D are four points on a horizontal field. A is north of B. The bearing of D from A is $${\small 115^{\large{\circ}}}$$ and the bearing of D from B is $${\small 25^{\large{\circ}}}$$. $${\small \angle {BDC} = 130^{\large{\circ}}}$$, BD $$=$$ 150 m and CD $$=$$ 110 m.
$${\small\hspace{1.2em}\left(a\right).\hspace{0.8em}}$$ Find the value of $${\small \angle {ADB}}$$.
$${\small\hspace{1.2em}\left(b\right).\hspace{0.8em}}$$ Find the bearing of B from D.
$${\small\hspace{1.2em}\left(c\right).\hspace{0.8em}}$$ Find the bearing of C from D.
$${\small\hspace{1.2em}\left(d\right).\hspace{0.8em}}$$ Calculate the shortest distance of point A to line DB.
$${\small\hspace{1.2em}\left(e\right).\hspace{0.8em}}$$ Calculate the length of BC.
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$${\small 8. \enspace}$$ In the diagram (not drawn to scale), E, G and C represents three points at the Esplanade, Gardens by the Bay and the City Hall respectively. Given that EG $$=$$ 1125 m and CE $$=$$ 957 m, the bearing of G from E is $${\small 135^{\large{\circ}}}$$ and $${\small \angle {CEG} = 60^{\large{\circ}}}$$. Find
$${\small\hspace{1.2em}\left(a\right).\hspace{0.8em}}$$ the bearing of E from C,
$${\small\hspace{1.2em}\left(b\right).\hspace{0.8em}}$$ the distance between C and G,
$${\small\hspace{1.2em}\left(c\right).\hspace{0.8em}}$$ $${\small \angle {EGC}}$$,
$${\small\hspace{1.2em}\left(d\right).\hspace{0.8em}}$$ the bearing of C from G.
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$${\small 9. \enspace}$$ In the diagram, Q is due east of P. Given that PQ $$=$$ 55 m and RQ $$=$$ 32 m and $${\small \angle {PRQ} = 105^{\large{\circ}}}$$. Find
$${\small\hspace{1.2em}\left(a\right).\hspace{0.8em}}$$ The bearing of R from P,
$${\small\hspace{1.2em}\left(b\right).\hspace{0.8em}}$$ The area of $${\small \triangle {PRQ}}$$.
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$${\small 10.\enspace}$$ In the diagram, A, B, C and D are four corners of a field. AD $$=$$ 53 m, DC $$=$$ 87 m, BC $$=$$ 66 m, $${\small \angle {ABC} = 90^{\large{\circ}}}$$ and $${\small \angle {ACB} = 58^{\large{\circ}}}$$.
$${\small\hspace{1.2em}\left(a\right).\hspace{0.8em}}$$ Calculate AC.
$${\small\hspace{1.2em}\left(b\right).\hspace{0.8em}}$$ The bearing of B from C is $${\small 340^{\large{\circ}}}$$. Calculate
$${\small\hspace{2.8em}\left(i\right).\hspace{0.7em}}$$ the bearing of A from C,
$${\small\hspace{2.8em}\left(ii\right).\hspace{0.7em}}$$ the bearing of A from B.
$${\small\hspace{1.2em}\left(c\right).\hspace{0.8em}}$$ Calculate
$${\small\hspace{2.8em}\left(i\right).\hspace{0.7em}}$$ the angle of $${\small \angle {ADC}}$$,
$${\small\hspace{2.8em}\left(ii\right).\hspace{0.7em}}$$ the area of $${\small \triangle {ADC}}$$,
$${\small\hspace{2.8em}\left(iii\right).\hspace{0.5em}}$$ the shortest distance from A to DC.
$${\small\hspace{1.2em}\left(d\right).\hspace{0.8em}}$$ An eagle is hovering vertically above A. The angle of elevation of the eagle from D is $${\small 42^{\large{\circ}}}$$. Calculate the greatest angle of elevation of the eagle from a point on DC.
$$\\[1pt]$$ As always, if you have any particular questions to discuss, leave it in the comment section below. Cheers =) .

1. Amina start from a point x and walks 220 on a bearing of 63 she then walks to a bearing of 63 she then walks to a point y on a bearing of 156 if y is due east of x find xy

2. Two walkers Kurt and Peter both observe a distant landmark. From Kurt the bearing
of the landmark is 210°T and from Peter the bearing of the landmark is 315°T. Peter
is standing 700m due south of Kurt.
i. Draw a well labelled diagram to represent this problem. (2 marks)
ii. Find correct to the nearest metre, the distance from Kurt to the landmark.

3. Village P is 25km on a bearing of 090°from village Q. Village R is 20km and on a bearing of 225°from village Q. Draw a sketch diagram of the relative positions of villages P, Q and R.

4. Village P is 25km on a bearing of 090°from village Q. Village R is 20km and on a bearing of 225°from village Q. Draw a sketch diagram of the relative positions of villages P, Q and R.

5. A girl starts at A and walks 2km south to B. She then walks 3km west to C. Find the distance and bearing of C from A

6. Mathematic.A boy moves from a point A to another point B, a distance of 20km in the direction N55⁰W. He then changes direction and move to a point C on a bearing of 240⁰.If the point C is directly due West of A , find (i)the distance BC(ii)distance AC

1. The bearing of A from B is 129° and the bearing of C from B is 225°. If B is equidistant .
A. Represent this information on a diagram
B. From the diagram, find the bearing of C from A

7. Two ships left a point x at same time ship a move 90 km away from x on m bearing of N 50°w while ship b 50km away from x on bearing of 75°.calculate how far from each other ship

8. The bearing of p&q is 036°. What is the bearing of Q from p

1. The bearing of A from B is 129° and the bearing of C from B is 225°. If B is equidistant .
A. Represent this information on a diagram
B. From the diagram, find the bearing of C from A

9. The bearing of p&q is 036°. What is the bearing of Q from p.

10. A girl stands facing south then turns in a clockwise direction through 120° to face the sun ,what is:
A. The surveyor’s bearing of the sun from the girl?
B. The compass bearing of the sun from the girl.

1. The bearing of A and B from a point p are 225 degrees and 116 degrees respectively. Ship A is 3.9km from ship B on a bearing of 258degrees. Calculate the distance of ship A from p

1. The bearing of A and B from a point p are 225 degrees and 116 degrees respectively. Ship A is 3.9km from ship B on a bearing of 258degrees. Calculate the distance of ship A from p

1. Gouu

11. The bearing town x from y is s50E.what is the bearing of y from x

12. hxdf

13. Sketch the ships journey ? If the ships leaves pa port A and travels on a bearing of 113 degrees to port B and then travels on a bearing of 172 degrees to another port C 305 km away

1. The bearing of A and B from a point p are 225 degrees and 116 degrees respectively. Ship A is 3.9km from ship B on a bearing of 258degrees. Calculate the distance of ship A from p

14. Tanks for ur light to my darkness on bearing

15. The bearing of Ibadan from Abeokuta is 060°. what is the bearing of Abeokuta from Ibadan

1. 360°-120°=240°

2. Hey sorry can you teach me bearing

16. An aeroplane leaves an airport A and flies on a bearing 036 degree for 1¹/2 hours at 600km/h
To an airport b it then flies on a bearing 130degree for 1¹/2 hourß at 400km/h to an airport
Calculate the distance from c to a

1. Village P is 25km on a bearing of 090°from village Q. Village R is 20km and on a bearing of 225°from village Q. Draw a sketch diagram of the relative positions of villages P, Q and R.

17. Comment A traveller move from a town p on a bearing of 055 to a town q, 200km away. He then moves from q on a bearing of 155 to a town r, 400km from q find (a) the distance between p and r (b) the bearing of p from r correct to the nearest degree

18. Two ship leaves a port at the same time on travels at 5km/h on bearing of 046° the other travels at 9km/h on the bearing of 127°. How far apart are the ship after 2 hours?

1. Amina start from a point x and walks 220 on a bearing of 63 she then walks to a bearing of 63 she then walks to a point y on a bearing of 156 if y is due east of x find xy

19. N is north of S. NS is the tangent to the circle, radius 1 km, at T. A man walks 2 km along the circle from T to P. What is the distance and bearing of P from T?

20. a ship sail, 50 km north from a point A, then 25km West and finally 50km on a bearing of 315° (i) how far west is the ship from the point A? (ii) how far north is the ship from the point A? (iii) find the distance and bearing of the ship destination from A.

1. Check out the solution here, Okasa:

https://youtu.be/B98wYbiyGas

Don’t forget to subscribe and follow my youtube channel for more video solutions!
uptuition with mr will

Cheers =)

21. the bearing of A from B is 129° and the bearing of C from B 219°. if B is equidistant from A and C, find the bearing of C from A

1. a ship sail, 50 km north from a point A, then 25km West and finally 50km on a bearing of 315° (i) how far west is the ship from the point A? (ii) how far north is the ship from the point A? (iii) find the distance and bearing of the ship destination from A.

1. Check out the solution here, Okasa:

https://youtu.be/B98wYbiyGas

Don’t forget to subscribe and follow my youtube channel for more video solutions!
uptuition with mr will

Cheers =)

2. A girl starts from a point x and walks 220m on a bearing of 063°.she then walks to another point y on a bearing of 156°.calculate |xy|

3. A ship sail from p,travels 100km in the direction N65 degree W to q and 70km north to r.Find the bearing and distance of r from p.

2. Check out the solution here, Okasa:

Don’t forget to subscribe and follow my youtube channel for more video solutions!
uptuition with mr will

Cheers =)

23. A,B,C,D are four locations on the same horizontal plane. B is on a bearing of 041° from A and the distance is 40km. D is 25km from C on a bearing of 074°. C is directly due north of A and the distance between B and C is 35km. Find the bearing of C from B.

1. Check out the solution here, Linda:

https://youtu.be/zfdWRQ-wXho

Don’t forget to subscribe and follow my youtube channel for more video solutions!
uptuition with mr will

Cheers =)

24. An aeroplane flies from town X on a bearing of 45*E to another town Y ,a distance of 200km.It then changes course and flies to another town Z on a bearing of S60*E , If Z is directly east of X ,calculate correct to 3s.f; A)the distance from X to Z. B)the distance from Y to XZ

1. Check out the solution here, Hamzat:

https://youtu.be/gjXiCbt4JTk

Don’t forget to subscribe and follow my youtube channel for more video solutions!
uptuition with mr will

Cheers =)

1. If the bearing of city a from city b is 043decree what is the bearing of city a

2. The bearing of town x from y is s50E.what is the bearing of y from x

25. Town A is at a distance of 400km° and of a bearing of 045° from town C.
(a) Draw an accurate diagram showing the positions of the three towns. (use a scale of 1cm to represent 50km)
(b) Determine the distance of bearing of town B from town A using a diagram.
(c) Jane live town C and drives an accurate speed of 80km/hr. At the same time, Rose leaves town A to town B and drives at 10km/hr who arrived at town B earlier

26. A ship leaves aport A and travels 215km on a bearing of 113° to port B and then travels on a bearing of 172° to another port C , 305km away.
a)sketch the ship’s journey
b)calculate the distance from A to C
c)what is the bearing from port C to port A?

27. A hunter walked into a bush on a bearing of 020 to reach a hut h 600 m from his home.He then walked 500 m on a bearing of 115 to trap t.
1.the distance of the trap from the home
2.the bearing of the trap from the home
3.the bearing of the home from the trap
4.the bearing of the hut from the trap

28. The bearing of a point Q from a point R is 074°what is the bearing of R from Q.

29. A student cycles 14km east from A and then 10km south-east to B.find the distance and bearing of B from A

1. point B is on a bearing of 041 from A and the distance is 40km .C is directly due north of A and the distance between B and C is 35 km . find the bearing of C from B and find the distance between A and C

30. an aeroplane left a city P on a bearing of 330 degree to a city Q a distance of 8km. it then changes direction and flew to another city R on a bearing of 250 degree, a distance of 60km. calculate how far the aeroplane is from the starting point. calculate the bearing of R fromP. calculate how far north of P is Q. calculate how far west of P is Q.

1. A city K is 200km from a city T in the direction 080 what is the bearing of T from K

31. A chord is 8.4cm long is 5.6 cm. From the centre of a find the radius of the circle

32. Comment Town A is 40km north and 25
km east of town B.What is the bearing of A from B

33. How can I solve the shortest distance in bearing

34. a man start from point X on a bearings of 56 degree to point Y of about 58km on the bearings of 164 degree to point Z of about 28km calculate the distance Z from X

35. A man walk due west for 4km. He then changes direction and walk on a bearing of 197 until he is south west of his starting point. How far is he from his starting point

1. What do they mean when they say how far east of Y is Z and how do I calculate it?

36. 1cm to 20km is used find the distances and bearings of p,q,r,s and t from o

37. 1cm to 20km is used , find the distances and bearings of p,q,r,s and t from o

38. An aeroplane flies for 4hrs from position P on a bearing of North 60 degree west to a point Q at an average speed of 60km/h.
The aeroplane then flies on a bearing of 150 degree Q to another point R 500km away. Calculate correct to 3 significant figures and show the diagram.
( a) the distance PR
(b) the bearing of R from P

39. A man start from a point x and walks 285m to y on a bearing of 078. He then walks due south to a point z which is 307m from x. Illustrate the information on a diagram. Find the bearing of x and z and find the distance between y and z.

1. A car travels from town P for 50km due North to town Q. It then travels 80km on a bearing of 270° to town R.
Calculate the shortest distance from town P to town R.

40. The bearing of A from B is 192 degrees. What is the bearing of B from A?

41. Two boats leave a port at the same time. The first leaves at 15km/hr on a bearing 135° while the second travels at 20km/hr on a bearing 063°. If after 2hours, the second boat is directly north of the first boat. Calculate their distance apart.

42. Pls help me with this I don’t understand,a students works 50m on a bearing of 25degrees and then 200m due east,how far is she from her starting point

43. Weldon sir\ma please i need your help i need a teacher for this topic

1. Explain more on it

1. A student cycles 14km east from A and then 10km South East to B. Find the distance and bearing of A from B

2. Pls help me solve this ;
Enugu is 450km due south of kaduna. Lagos is due west of enugu and on bearing 225 degree from kaduna. Pls help calculate the distance between Lagos and enugu.

1. While in the city centre amina would wish to go to bank of uganda which is of uganda which is 240m away from the city centre of bearing of 300degree from the same point she also has to meet her uncle in the new taxi park which is 300m on abearing of252 degrees from the city centre using a scale of lcm for 40m show aminas route by scale drawing

44. Weldon sir\ma please i need your help i need a teacher for this topic

45. Two boats A and B left a port C at the same tie on dfferent routes.B travelled on a baring of 150 and A travelled on north side of B. When A had travelled 8km and B travelled 10km, the distance between the btwo boats was found to be 12km. Calculate the bearing of A’s route from C

1. Check out the solution here, Jackson:
https://www.instagram.com/p/CPCfSNEBhek/

Cheers =)
uptuition with mr will

46. An aircraft travels 120km on a bearing of 062° and then 95km on a bearing of 305°. How far is the aircraft from the starting point

1. Check out the solution here, Kopji:
https://www.instagram.com/p/CPCfGwHBodI/

Cheers =)
uptuition with mr will

2. The distance and bearing of port A and B from p are (3k, 025) and (20km, 295) respectively. Calculate the distance/AB/ between the two to the nearest km

47. An aircraft travels 120km on a bearing of 062 and 95km on a bearing of 305. How far is the aircraft from its starting point

1. Iam requesting for answers for while in the city centre

48. Comment how do they solve this

49. Two men p and q set of a base camp R prospecting from oil.P moves 20km on a bearing 205 degree and Q moves 15km on bearing 060 degree to calculate the distance of Q from P and the bearing of Q and P

1. Comment how do they solve this

50. A navy ship leaves port A on a bearing of 120° and travels 200 kilometers to port B.it then travels 250 kilometers from port B to port C on a bearing of 225°.
¡)Draw a diagram that best represents the route of the ship.
¡¡)Calculate the direct distance from port A to port C to the nearest kilometer.

1. How do they solve this problem

51. A man sets to travel from P to R via Q. From P he travels a distance off 12 kilometres on a bearing 30 degree to q. From q he then travels a further 5 km due east. I. How far R is North of p. I I how far r is East of p. III. Evaluate pr

52. an aeroplane flew from a city X on a b X earing 225° to another city Y a distance 200km away. it then flew from city Y or a bearing of N30°W to city Z a distance of 250km. calculate: (1) the distance from city X connect to the nearest whole number. (2) the bearing of city X from Z

1. Commenting iam in trouble its getting me mad

53. Please somebody,anybody answer this question for me. Three towns XYZ are such that the distance between X and Y is 15Km and the distance between X and Z is 9 Km.If the bearing of Y from X is 70°and the bearing of Z from X is 310°.Calculate;
(i)the distance between Y and Z
(ii)the bearing of Z from Y
(iii)the bearing of Y from Z

1. A man obserb the top bottom of a story building from the top of a non story building. He observe that the angleof alabition of the story building is 470degree while the angle of the depression to the bottom of the story building is 40degree if the 2 building a 50m a part find the
1-The highest of the non story building
2-the high of the story building correct to the three significant figure

1. I DONT UNDERSTAND EITHER.

54. Three towns XYZ are such that the distance between X and Y is 15Km and the distance between X and Z is 9 Km.If the bearing of Y from X is 70°and the bearing of Z from X is 310°.Calculate;
(i)the distance between Y and Z
(ii)the bearing of Z from Y
(iii)the bearing of Y from Z

55. I don’t understand the 9th problem :(( How can it be solved?

1. 9. In the diagram, Q is due east of P. Given that PQ = 55 m and RQ = 32 m and ∠PRQ=105∘. Find
(a). The bearing of R from P

How do I find a?

1. never mind. ive solved it already :))

56. Hello I need help
Town F is 50 km east of town G
Town H is on a bearing of 040 from Town F.
The distance from F to H is 65 km

Calculate ,to the nearest km, the actual distance GH .
Calculate, to the nearest degree, the bearing of H from G.

1. Check out the solution here, Asia:
https://www.instagram.com/p/CMU0DKEllAC

Cheers =)
uptuition with mr will

2. A student cycles 14km east from A and then 10km south-east to B.find the distance and bearing of B from A

57. From a point H at a harbour,the bearing of two ship A and B,on the high sea are 160 and 220 respectively.B is 14km from H and bearing of A from B is 85
How far apart are the two ships.
What is the bearing of B from A

1. Check out the solution here, Precious:
https://www.instagram.com/p/CMgdBoclhWh/

Cheers =)
uptuition with mr will

58. b) The bearing of a ship
R
from a port
P
is 280⁰ and its bearing from a town
T
is
010 .
If the town
T
lies due west of the port
P,
find the bearing of
(i) T from
R

1. Mathematic.A boy moves from a point A to another point B, a distance of 20km in the direction N55⁰W. He then changes direction and move to a point C on a bearing of 240⁰.If the point C is directly due West of A , find (i)the distance BC(ii)distance AC

59. A ship leaves a port at noon and has a bearing of 207 degree. If the ship is traveling at 20 miles per hour, how many miles south and how many miles west is the ship from it’s departure point at 6 pm?

1. Check out the solution here, Joshua:
https://www.instagram.com/p/CMgc_U1ls3P/

Cheers =)
uptuition with mr will

2. I don’t understand the work.

3. Mathematic.A boy moves from a point A to another point B, a distance of 20km in the direction N55⁰W. He then changes direction and move to a point C on a bearing of 240⁰.If the point C is directly due West of A , find (i)the distance BC(ii)distance AC

60. Please can u help me with this question. The bearing of two point Q and R from a point P are 050 and 120 respectively if [PQ]=12cm and [PR]=5cm,find the distance QR

1. Check out the solution here, Anon:
https://www.instagram.com/p/CMgc9WxlqxU/

Cheers =)
uptuition with mr will

61. the bearing of city R from city M is 0.58degres and the bearing of city K from city M is 310degres if the distance from M to R is 40km and that of M to K is 70km what is the distance between K and R to 1 decimal place and bearing of K from R to the nearest degree

1. Check out the solution here, Iliyasu:
https://www.instagram.com/p/CMgc7IcFcdM/

Cheers =)
uptuition with mr will

62. A village R is 10km from a point P on a bearing 025 degrees from P. Another village A is 6km from P on a bearing 16 degree. Calculate
a) distance of R from A
b) bearing of R from A

1. Check out the solution here, Promise:
https://www.instagram.com/p/CMgc4Tnl78K/

Cheers =)
uptuition with mr will

63. This was really helpful thank you so much

64. Help me with this question.factorise 5b_3

65. A ship is 4km due north and then 3km on a bearing of 60°.find the distance from his original position.

1. You can take a look at my explanation below:
https://youtu.be/I2QdTbg_7-M

Cheers,
Mr Will

2. I need the solution

66. I need ur help

1. mohammed treks 3km from point A on a bearing of 023°. he then treks 4km on a bearing of 113°to a point B. what is the bearing of B from A ?

2. In PQR, the length of side. PQ=
PR=12cm. QR=7CM find PQ

67. A boat sails round a quadrangular course ABCD, starting from A to B in4km due east of A,C 3km due South of B and D 4km S50W from C.what is the distance and bearing of A from D?

1. You can take a look at my explanation below:

Cheers,
Mr Will

68. I don’t know the Calculation at all and how can I coz is coming out in Waec(Exam)…pls I need your help sir or ma??????

1. Hi Joseph,

Just keep revising and make sure you understand the basic first.

You can take a look at your textbooks, study notes or even the summary notes and exercise examples I have written here.

Good luck for your exam and cheers!

Mr Will

69. how can some1 know the full understanding of bearing and distance calculation

70. 1.A village is 10km on a bearing 0500 from a point o , how far is the village North of o .
2.The angle of elevation of the top of a building from a point 80m away on a level ground is 25°.calculate the height of the building to the nearest metre.

1. You can take a look at my explanation below:
https://youtu.be/A7f7mjSoeuY

Cheers,
Mr Will

71. The bearing of a town Y from X is 125°, find the bearing from X to Y

72. Nice and awesome thanks Mr. Will

1. You’re welcome ?
Mr Will

2. D is 30km due east of A. A ship sails from A on a certain bearing of 15km to B it then sail to C which is 40km from A and due north of D. Finally it sails due south of D. AB is a bisector of angle EAC. Calculate the total distance for the whole journey.

73. three town A B C are such that the distance between A and B is 50km and the distance between A and B is 90km. if the bearing of B from A is 75degree and the bearing of C from A is 310degree find the @ distance between B and C (b)bearing of C and B

74. unable to solve this
B is 48 km West and 31 km south of A. Calculate the bearing from B to A.

An aeroplane X whose average speed is 50°km/hr leaves Kano air port at 7:00am and travels for 2 hours n a bearing 050°. It then changes its course and flies on a bearing 1200 to an airstrip A.
Another aeroplane Y leaves Kano airport at 10:00am and flies on a straight course to the airstrip A. Both planes arrives at the airstrip A at 11:30am. Calculate
(A)the average speed of Y to three significant figures
(B) the direction of flight Y to the nearest degree

76. please can you help me with this question P,Q,R,S are four locations on the same horizontal plane Q is on a bearing of 041 degrees from P and the distance is 40 kilometres S is 48 kilometres from R on a bearing of 074 degrees.R is directly due north of P and the distance between Q and R is 38 kilometres find
(a) the bearing of R from Q
(b) the distance between Q and S
(c) the distance between P and R

77. A ship leaves port p and sails on a bearing N50°E to a port Q 15km away. It then sails on a bearing of S45°E to port R, 20km away

1. pls u put only the question u did nt specify on what we are to look for

78. IS VERY GOOD

79. IS GOOD

80. Two ships A and B leaves a port simultaneously. A steams at 10kmh^-1 on the bearing of 215. After one hour, the bearing B from A is 260. Find the speed of B

81. If a ship leaves aport A and travels 215km on a bearing of 113 degrees to Port B and then travels on a bearing of 172 degrees to another Port C, 305km away.What will be the sketch of the ship’s journey?.Show the diagram sketch of the ship.

1. A car travels from town p for50km due north to town q . It then travels 80km on a bearing of 270 to town r. Calculate . The shortest distance from p to town r , the bearing of town r from p ,the bearing of p from r

82. A surveyor observes that the bearing of a beacon O from two other beacons P and Q are . N30degreeW and N70degreeE respectively. If the bearing of P from Q is 080degree and PQ = 300m. Calculate (a)the distance PQ (b)the distance of O from PQ (c)the bearing of Q from P