Question

ABC and D are four towns

B is 25km due east of A
C is 25km due north of A
D is 45km due south of A

work out the bearing of B from C ​

Answer 1

225°

Explanation:

In mathematics, a bearing is defined as an angle measured clockwise from north.

See attached graph for a clearer guide to the explanations

Angle ABC is a right isosceles triangle with AB = 25 and AC = 25

m∠BAC =90°

So m∠ABC = m∠ACB = 45°

The angle at BC is 45° from the North (90°-45°) measured clockwise is 45° so we say the bearing from C to B is 045° (we use 3 digits for bearing)

The bearing from B to C on the other hand is determined by adding 180° to the bearing in the opposite direction (C to B) so the bearing from C to B is 180° +045° = 225°

(Here I am not sure whether you are supposed to answer the question in mathematical meaning of bearing or just state the direction in which BC lies relative to north. 45° clockwise from the North is in a NE direction so we can say C is NE from B but I am guessing that's not it)

Answer 2

213.7°

Explanation:

The bearing of B from D is angle ADB, which is ∠ADB = arctan(30/45)

≈ 33.7°

The bearing of D from B is that angle plus 180°, so is 180° +33.7° = 213.7°