Precalculus: triangle word problem

Question

A sailboat leaves port on a bearing of S72 degrees W. After sailing for two hours at 12

knots, the boat turns 90 degrees toward the south. After sailing for three hours at 9 knots on this course, what is the bearing to the ship from port? Round your answer to the nearest 0.1 degree.

Answer 1

Hi Katelyn A.,

The path of the sailboat forms a right triangle with the first leg equal to, 2 hours*12 knots, or 24 nautical miles. And the second leg equal to 3 hours*9 knots = 27 nautical miles.

You can find the angle of the triangle at the port to be tan^-1(27/24) = 48.366^o.

72^o - 48.366^o = 23.6^o (rounded to 0.1). Therefore the sailboats bearing at this time is S23.6^oW.

I hope this helps, Joe.