Orders of Magnitude and Bearing

Bearing is always calculated from the north in a clockwise direction. Bearing is always a three digit numbers.

Draw the following bearing of
a) 0600 from A to B c) 2400 from P to Q
b) 1100 from P to Q d) 3000 from X to Y.

Answer the following questions.
1. The bearing of B from A is 0650. Find the bearing of A from B.

2. The bearing of Y from X is 1350. Find the bearing of X from Y.

3. The bearing of P from Q is 2200. Find the bearing of Q from P.

4. The bearing of A to B is 3100. Find the bearing of B to A.

5. The bearing of X to Y is 0750. Find the bearing of Y to X.

6. The bearing of A from B is 2600. Find the bearing of B from A

7. The bearing of Q from P is 1250. Find the bearing of P from Q.

8. The bearing of W to X is 3350. Find the bearing of X to W.

Write down the bearings using the angles given the figures.

1. a) Write down the bearing of B from A b) Write down the bearing of A from B

2. a) Write down the bearing of Q from P b) Find the bearing of P from Q

3. a) Find the bearing of F from E b) Find the bearing of E from F.

4. a) find the bearing of G to H b) find the bearing of H to G

5. a) Find the bearing of B from A. b) Find the bearing of B from C. c) Find the bearing of A from B. d) Find the bearing of C from B.

6. a) find the bearing of Q from P. b) find the bearing of R from Q.

c) find the bearing of P from Q. d) find the bearing of Q from R.
7. a) find the bearing of tanker from the light house. b) find the bearing of tanker from the yacht. c) find the bearing of light house from the yacht.

8. a) find the bearing of the ferry from the light house. b) find the bearing of the harbour from the ferry. c) find the bearing of the light house from the ferry.

d) find the bearing of harbour from the light house. e) find the bearing of the light house from the harbour.

9. A boat (A) sales 75 km due north to port B. It then sales 65 km due east to port C. a) Find the direct distance AC b) find the bearing of C from A. c) find the bearing of A from C.

10. A submarine leaves the port A due east a distance of 80 km to port B. It then moves due south to port C which is 72 km away.

a) Find the direct distance AC.

b) Find the bearing of C from A.

11. A ship moves due west to port B a distance of 125 km, it then moves south to port C which is 100 km from B.
a) Find the distance taken if the ship travels directly from A to C.

b) Find the bearing of C from A.

12. A destroyer D and a ship C leaves the port P at the same time. The destroyer sales 25 km on the bearing of 0400 and the ship sales 30 km on a bearing of 3200. Find how far the two ships are.

13. From A, a ship moves 11 km on a bearing of 0410 to B. From the same point A another ship leaves on a bearing of 3410 a distance of 8 km to point C. Find the distance between B and C.

14. A plane and helicopter leaves the airport P at the same time. The aeroplane flies 250 km on a bearing 0400 and the helicopter flies 300 km on a bearing of 3200. Find how far is the aeroplane from the helicopter.

15. A boat sales 8 km from port P on a bearing of 0700. It then sales 5 km on a bearing of 0400. Calculate the direct distance of the boat from P.

16. An aircraft flies 70 km on a bearing of 0800. It then flies 110 km on a bearing of 0400 to reach its destination. Find the direct distance of the destination.

17. An aircraft flies from its base B a distance of 200 km on a bearing of 1620 to point C. It then travels 350 km on a bearing of 2600 to point D and returns to the base directly. Calculate the direct distance.

18. From a light house L an aircraft carrier A is 15 km away on a bearing of 1120 and a submarine S is on a bearing of 2000 and 26 km away from the light house. Find the distance between A and S.

19. A ship sales from port A on a bearing of 1350 a distance of 58 km to port B. Another ship sales from port A due south to port C a distance of 70 km. Find the distance between B and C.

Mixed Questions
1. In a triangle LMN, Angle LNM = 900, angle MLN = 280 and LM = 10 cm. a) Calculate i) MN ii) LN iii) area of triangle LMN.

2. In the diagram below ABD is a straight line. AB = 4m and AC = 6m, angle BAC =900. i) Use trigonometry to calculate angle ABC. ii) Angle CBD iii) Length of BC. iv) Area of triangle ABC.

3. A ship travels 50 kilometres from A to B on a bearing of 140°, as shown in the diagram. Calculate how far south B is from A.

4. a) Calculate the distance between B and R.

b) Calculate the bearing of R from B, correct to nearest degree.

5. Samira (S) and Tamara (T_) walk towards each other. Samira walks on a bearing of 140°. Find the bearing on which Tamara walks.

6. A plane flies from Auckland (A) to Gisborne (G) on a bearing of 1150. The plane then flies on to Wellington (W). Angle AGW = 630.

a) Calculate the bearing of Wellington from Gisborne.

b) The distance from Wellington to Gisborne is 400 kilometres.
The distance from Auckland to Wellington is 410 kilometres.
Calculate the bearing of Wellington from Auckland.
7. A straight road between P and Q is shown in the diagram. R is the point south of P and east of Q. PR = 8.3 km and QR = 4.8 km. Calculate a) the length of the road PQ,

b) the bearing of Q from P.

8. A railway line, between stations A and B, is straight and has a length of 4800 m. The bearing of B from A is 200 °. The point P is due east of B and due south of A. a) Complete the sketch above to show triangle ABP.

b) Calculate the length of AP.

9. Felipe (F) stands 17 metres from a bridge (B) and 32 metres from a tree (T).The points F, B and T are on level ground and angle BFT = 40°.

(a) Calculate
(i) the distance BT,

(ii) the angle BTF.

(b) The bearing of B from F is 085°. Find the bearing of
(i) T from F, (ii) F from T, (iii) B from T.

10. A ship sails 100 kilometres from A on a bearing of 0700 to B. It then sails 120 kilometres on a bearing of 1600 to C.

i) Show that x + y = 900.

ii) Use trigonometry to calculate the size of angle BAC.

iii) Find the three-figure bearing of C from A.

iv) Find the three-figure bearing of A from C.
11. Bashira lives in town A and works in town B, which is 13 kilometers from a on a bearing of 0400. She drives from house to work and then drives to visit her mother who lives in town C. Town C is 17 kilometers from B on a bearing of 1300 from B.

a) write down the value of p and q.

b) Calculate the size of angle ACB.

c) Calculate the distance CA.

d) Find the area of triangle ABC.

e) Find the bearing of A from C.

12. (a) During a soccer match a player runs from A to B and then from B to C as shown in the diagram.AB = 40m, BC = 45 m and AC = 70m.

(i) Show by calculation that angle BAC = 37°, correct to the nearest degree.

(ii) The bearing of C from A is 051°. Find the bearing of B from A.

(iii) Calculate the area of triangle ABC. (b) Another player is standing at D. BC = 45 m, angle BCD = 54° and angle DBC = 32°.

Calculate the length of BD.

13. A boat B is 1200 metres from a lighthouse L and 750 metres from a rock R. Angle LBR = 110°. (a) Calculate
(i) the length LR, correct to the nearest metre,
(ii) angle BLR, correct to the nearest degree. (b) The bearing of B from L is 053°. Calculate
(i) the bearing of L from B,
(ii) the bearing of B from R.

14. A and B are two points on a coastline. B is directly East of A.
A ship S can be seen from both A and B.
The bearing of S from A is 054°. The bearing of S from B is 324°.
(a) Find the number of degrees in
(i) angle SAB,
(ii) angle SBA.
(b) Use your answers to part (a) to show that angle ASB = 90°

15. The diagram shows the positions of four cities in Africa, Windhoek (W), Johannesburg(J),
Harari (H) and Lusaka (L).
(a) Calculate the distance LH.

(b) Calculate the distance WJ.

(c) Calculate the area of quadrilateral WJHL.

(d) The bearing of Lusaka from Windhoek is 060°.
Calculate the bearing of

(i) Harari from Windhoek,

(ii) Windhoek from Johannesburg.
16. The quadrilateral PQRS shows the boundary of a forest.
A straight 15 kilometre road goes due East from P to R.
(a) The bearing of S from P is 030° and PS = 7 km.
(i) Write down the size of angle SPR.

(ii) Calculate the length of RS.

(b) Angle RPQ = 55º and QR = 14 km.
(i) Write down the bearing of Q from P

(ii) Calculate the acute angle PQR.

(iii) Calculate the length of PQ.

(c) Calculate the area of the forest, correct to the nearest Km2
17. To avoid an island, a ship travels 40 kilometres from A to B and then 60 kilometres from B to C.
The bearing of B from A is 080° and angle ABC is 115°.
(a) The ship leaves A at 11 55.
It travels at an average speed of 35 km / h.
Calculate, to the nearest minute, the time it arrives at C.

(b) Find the bearing of
(i) A from B
(ii) C from B.

(c) Calculate the straight line distance AC.
(d) Calculate angle BAC.
(e) Calculate how far C is east of A.