Precalculus help

Question

A ship leaves port at noon and has a bearing of S 29º W. The ship sails at 30 nautical miles per hour. At 6:00 P.M., the ship changes course to due west. What is the ship’s bearing and distance from the port of departure at 7:00 P.M.?

Answer 1

For the first leg of the journey, the ship traveled 180 miles S 29° W. We need to find how far due west and south the ship traveled.

x = 180 sin(29°) = 87.266 miles west.

y = 180 cos(29°) = 157.43 miles south.

By 7:00 PM the ship has traveled 30 + x = 117.266 miles due west.

The distance will be the hypotenuse of the right triangle with height of 157.43 miles and base of 117.266 miles.

h = √((30+x)²+y²) = 196.30 miles

Bearing from port will be arcsin(117.266/196.3) = 36.68 --> S 36.68° W