Question

A boat sails for 30km on a bearing of 145 degree then 10 km on a bearing of 250 degree, calculate
(a) the distance covered from the starting point
(b) the bearing of the harbour from the ship

Answer 1

145 = 35 degrees south of west
250 = 70 degrees north of west

distance north = -30 sin 35 + 10 sin 70
distance west = 30 cos 35 + 10 cos 70

distance north = -17.2 + 9.4 = -7.8
distance west = 24.6 + 3.4 = 28
tan angle south of west = 7.8/28
angle south of west = 15.6
so compass bearing harbor to ship = 270 -15.6 = 254.4 deg
so PART B is 254.4 - 180 = 74.4 (about east by north)
range from start = sqrt (28^2 + 7.8^2)