A boat leaves port and heads out to sea on a bearing of 189

A boat leaves port and heads out to sea on a bearing of 189 degrees, sailing at 8 knots (i.e. at a speed of 8 nautical miles per hour). Another boat leaves port at the same time and travels on a bearing of 279 degrees at 15 knots. Find the distance between the two boats after 2 hours.

Solution

in 2 hours distance travelled by boat 1 = speed 1 * time = 8*2 = 16 nautical miles

distance travelled by boat 2 = speed 2 * time = 15*2 = 30 nautical miles

since two distances make right angle with each other

applying pythagoraean identity to solve

d^2 = 30^2 + 16^2

d^2 = 1156

d = sqrt 1156

d = 34 nautical miles

distance between 2 boats = 34 nautical miles