Find the bearing.

Question

Two ships left the same harbor. The first ship headed in the direction (North 16 degrees West) at 37.5 miles per hour. The second ship left one hour later at 48 miles per hour. If two hours after the first ship had left the harbor the two ships were 63 miles apart, what was the bearing of the second ship.

Answer 1

It's a triangle with sides 75, 48 and 63

side opposite 16 degrees is 63

use Law of Sines

sinA = 48sin16/63 = about .21

A = sin^-1(.21) = about 12.123 degrees

It's a 16 -12.123- 151.877 degree triangle

bearing of the 2nd =151.877-90

= 61.877 West of North