F3 -F 4 Maths

A sails on a bearing of 300 degree for 12km while ship B sails on a bearing of 150 degree for 12 (km) <--- is this km or m?

I'll just take it as km.

a)Angle made by the paths of the ships = (300 - 150) degree = 150 degree
Let y km be the distance between the two ships. By the Cosine Law,
y^2 = 12^2 + 12^2 - 2(12)(12)(cos 150)
y^2 = 288 + 144sqrt(3)
y = 23.18221983

So the distance between the two ships is 23.2 km (corr. to 3 sig. fig.)

b)Let C be the port.
angle CBA
= angle CAB (base angles, isos. triangle)
=(180 - 150)/2 degree
=15 degree

So the bearing of A from B
= (180 + 150 - 15) degree (refer to the fig linked below)
= 315 degree

c) The bearing of B from A
= The bearing of A from B - 180 degree
= 135 degree

fig:http://i207.photobucket.com/albums/bb173/kkkpopup/fig6.jpg