Solutions to New General Mathematics Exercises for SS2 on Bearing and Distance in Mathematics. (Sine and Cosine Rule)
Macrae, M. Kalejaiye, A.O. , Chima, Z.I., Garba, G.U., Ademosu, M.O. (2007). New General Mathematics: For Senior Secondary Schools. Pearson Education Limited.
To help you go over your workings as you study.

Introduction to Basic Concepts on Bearing and Distance in Mathematics - 00:01:29

Sine Rule Exercise 5c
1.) A point X is 34m due east of a point Y . The bearings of a flagpole from X and Y are N18˚W and N40˚E respectively. Calculate the distance of the flagpole from Y. - 00:24:14
2.) A man walks due west for 4km. He then changes direction and walks on a bearing of 197˚ until he is south-west of his starting point. How far is he then from his starting point? - 00:34:27
3.) A girl starts from a point A and walks 285m to B on a bearing of 078˚. She then walks due south to a point C which is 307m from A. What is the bearing of A from C, and what is |BC| ? - 00:49:12
4.) The bearing of a house from a point A is 319˚. From a point B, 317m due east of A, the bearing of the house is 288˚ . How far is the house from A? - 01:17:42
5.) The bearings of ships A and B from a port P are 225˚ and 116˚ respectively . Ship A is 3.9km from ship B on a bearing of 258˚ . Calculate the distance of ship A from P. - 01:30:25
6.) An aeroplane flies from a town X on a bearing of N45˚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 3 significant figures- 01:45:04
7.) A mass hangs from a horizontal beam by two strings... 01:56:53
8.) An aircraft is timetabled to travel from A to B. Due to bad weather it flies from A to C then from C to B, where (𝑨𝑪) ̅ and (𝑪𝑩) ̅ make angles 27˚ and 66˚ with (𝑨𝑩) ̅, If |AC| = 220km, calculate |AB|. 02:01:29
9.) Two wires support an electricity pole... 02:06:50
10.) From Points A and B on level ground, the angles of elevation of the top of a building are 25˚ and 37˚ respectively. If |AB| = 57m, calculate, to the nearest metre, the distances of the top of the building from A and B if they are both on the same side of the building. 02:15:14

Exercise 9e Cosine Rule
1) From a point on the edge of the sea, one ship is 5km away on a bearing S50˚E and another is 2km away on a bearing S60˚W. How far apart are the ships? - 02:29:32
2) A student walks 50m on a bearing 025˚ and then 200m due east. How far is she from her starting point? - 02:37:09
3) Two goal posts are 8m apart. A footballer is 34m from one post and 38m from the other. Within what angle must he kick the ball if he is to score a goal? - 02:47:11
4) City A is 300km due east of city B. City C is 200km on a bearing of 123˚ from city B. How far is it from C to A? - 02:52:34
5) A triangular field has two sides 50m and 60m long, the angle between these sides is 96˚. How long is the third side? - 03:02:41
6) Two boats A and B left a port C at the same time on different routes. B travelled on a bearing of 150˚ and A travelled on the north side of B. When A had travelled 8km and B had travelled 10km, the distance between the two boats was found to be 12km. Calculate the bearing of A’s route from C. - 03:07:43
7) A surveyor leaves her base camp and drives 42km on a bearing of 032˚. She then drives 28km on a bearing of 154˚. How far is she from her base camp and what is her bearing from it?-
03:18:48
8) Two ships leave port at the same time. One travels at 5km/h on a bearing of 046˚. The other travels at 9km/h on a bearing of 127˚. How far apart are the ships after 2hours? - 03:35:12
9) A boat sails 4km on a bearing of 038˚ and then 5km on a bearing of 067˚.
How far is the boat from its starting point?
Calculate the bearing of the boat from its starting point. - 03:46:25
10) A photographer is 350m away from a lion and wants to get closer before he takes a photograph. There is a water-hole in the direct line between the lion and himself, so he moves at an angle of 8˚ to this line to a better position 200m further on. Calculate his distance from the lion. - 04:02:57
11) Two planks of lengths 1m and 1.2m, lean against each other as shown... - 04:11:36
12) An aeroplane flies due north from Ikeja Airport for 500km. It then flies on a bearing of 060˚ for a further distance of 300km before overflying a road junction. - 04:19:39
13) A ship leaves port and travels 21km on a bearing of 032˚ and then 45km on a bearing of 287˚.
Calculate its distance from the port.
Calculate the bearing of the port from the ship. - 04:35:30
14) An aircraft flies round a triangular course. The first leg is 200km on a bearing of 115˚ and the second leg is 150km on a bearing of 230˚. How long is the third leg of the course and on what bearing must the aircraft fly? - 04:55:01
15) Villages A, B, C, D, are such that B is 4km due east... - 05:11:54
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