The bearing of two villages A and B. From a health centre. H are 045° and 285° respectively |HA|=9km and |HB|=6km. Calculate the: 1.distance of B from A 2. Bearing of A from B

northeast and about west by north (15 deg north of west which is 270)

so angle AHB = 180 - (45+15) = 180 - 60 = 120 degrees
law of cosines
AB^2 = BH^2 + AH^2 - 2 * BH * AH cos 120
AB^2 = 36 + 81 - 2*6*9 * (-0.5)
= 117+ 54 = 171
so
AB = 13.1 km

then
sin B / 9 = sin 120/ 13.1
etc