Which are the possible courses for the sailboat.

Question

A sailboat set a course of N 25° E from a small port along a shoreline that runs north and south. Sometime later the boat overturned and the crew sent out a distress call. They estimated that they were 14 miles away from the nearest harbor, which is 32 miles north of the port they had set sail from. If a rescue team leaves from the harbor, find all possible courses the team must follow in order to reach the overturned sailboat. (Select all that apply.)

S 40° E

S 50° E

S 10° E

N 80° E

S 80° E

Answer 1

You can draw a triangle ABC modelling this. A is the starting point of the boat, B is the harbor location, C is the current boat position. AB is 32, BC is 14 and angle A is 25 degrees. AB runs due north.

You need to find the angle B.

To do that use sine rule to find angle C then take C and A away from 180. Knowing angle B you can find the direction(s).

Sine rule : a/sin A = b/sin B = c/sin C.

So here 14 / sin 25 = 32 / sin C

You can complete this as an exercise.

Mike