A ship leaves port at 5 am and heads due east at 23 knots. At 10 am, to avoid a storm the ship changes course to N 60° E 60° east of north Find the ships distance from port at 4 pm. Round to the nearest tenth.

Question

A ship leaves port at 5 am and heads due east at 23 knots. At 10 am, to avoid a storm the ship changes course to N 60°  E  60° east of north Find the ships distance from port at 4 pm. Round to the nearest tenth.

Reiny · Answer

make a sketch
distance along first direction = 5 hrs x 23 knots
= 115 n miles
distance along 2nd direction = 6(23) = 138 n miles
angle between the two directions = 150°

by cosine law:
x^2 = 115^2 + 138^2 - 2(115)(138)cos 150°
= 59756.64...
x = 244.45 nautical miles
= appr 244.5 n miles