Question

three towns A,B,C are situated such that AB is equal to 60km and AC is 100km.The bearing of C from A is 290degree and the bearing of B from A is 060 degree calculate
a)the distance BC
b)the bearing of B from C

Answer 1

use the law of cosines to get BC, knowing that angle a is 130 degrees.

then use the law of sines to get angle B, and then you can figure the bearing of C.

Answer 2

All angles are measured CW from +y-axis.
Given: AB = 60 km[60o], AC = 100 km[290o], BC = ?
BC = BA + AC = 60[60+180] + 100[290o]
BC = ( 60*sin240+100*sin290) + (60*cos240+100*cos290)I
BC = -146 + 4.2i = 146.1km[-88] = 146.1km[272o].
CB = 146.1km[272-180] = 146.1km[92o].