Question

. From A, B lies 11 km away on a bearing of 041° and C lies 8 km
away on a bearing of 341°. Find:
a) the distance between B and C
b) the bearing of B from C.​

Answer 1

Answer:

if you lay the points on a circle with origin at A, you will get a triangle with an interior angle of 60 deg at A, which is the sum of the bearing of 41 deg between A and B, and 360deg-341deg= 19 deg, the beraing between points A and C. let a be the side opposite to angle A at point A, you know the distances between A and B call that side

c =11km opposite to angle C, and side b =8km opposite to angle B.

Using the law of cosines:

a2 = b2 + c2 - 2 bc cos A

a2 = 82 + 112 - 2 (8)(11) cos 60

a2 = 97, a = 9.8 km

Now you need the bearing of B from C

From the law of Sines find the angle C at point C

9.8/sin60 = 11km/sin C, sin C = (sin60x11km)/(9.8km)=0.972

sin-1sin C = 75.3 degrees

The bearing of B from C is the angle formed by the line joining C and B and rotating about C. By Geometry this angle is

180 - sum( Angle C + 19 deg ) = 180-(75.3+19)=85.7 deg