Question

Two ships A and B left a port each with a uniform speed on bearing 045 degree and x degree respectively. After 4hrs, they covered 100km and 120km respectively with B on a bearing of 105 degree from A. Calculate correct to 1 decimal place the value of x

Answer 1

Draw the diagram. You can see that the angle at A is 120°
You can find the angle at B using the law of sines:
sinB/100 = sin120°/120
Now, you know that
x-45 + 120 + B = 180

Answer 2

All angles are measured CW from +y-axis.
Given: PA = 100km[45o].
PB = 120km[Xo].
Bearing AB = 105o.

A = 105-45 = 60o = angle between PA and AB.
sin B/100 = sin60/120
B = 46.2 degrees.

P = 180-A-B = 180-60-46.2 = 73.8 degrees.
X = 45+P = 45+73.8 = 118.8 degrees.