Trigonometry bearings

Question

Three supermarkets A B and C lie in the same horizontal plane and are positioned such that:

B is 6 km from A on a bearing of 015 degrees,

C is on a bearing of 045 degrees from A,

The distance between B and C is 14 km.

Calculate

a)the distance of C from A( 3 marks )

b)the bearing of C from B to the nearest degree ( 4 marks )

Please show working out. Thank you :)

Answer 1

Draw and label a diagram!

What is the measure of angle BAC?

Use that with Law of Cosines to determine AC

Use Law of Sines to determine measure of angle ABC

Then calculate bearing of B to C