3 town a,b,c are situated so that ab=60km,ac=100km.the bearing of b from a is 60degree& c from a is 290degree

Question

Find the distance of BC.find the bearing of B from C

Answer 1

In triangle ABC, AB=60km, AC=100km and angle A is 360-(290-60)=130 degrees.

Cosine rule: BC^2=AB^2+AC^2-2AB.ACcos130=3600+10000+12000cos50=21313.45

BC=145.99km. Bearing is -070 or N70W.

Bearing of B from C is found using the sine rule:

sinC/60=sin130/145.99, sinC=0.3148 approx., so C=18.35 degrees.

To get the bearing of B we add 70 degrees to this=88.35 degrees. This gives the bearing from the south, so to get the bearing from the north we subtract from 180=91.65.