What are the possible courses?

Question

Which are the possible courses for the sailboat?

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

Here are sketches of each answer. We need to use the Law of Sines to determine if these are all possible triangles.

The Law of Sines uses the sine of the angle divided by the opposite side length. Each triangle has sin(25)/14 which is 0.0302 so we look for triangles that maintain this number for the other angle/side ratios

For triangle A. Angle x = 180-40-25 = 115 and sin(115)/32 = 0.0283 Not the same so not possible

For triangle B, Angle x = 105 and sin(105)/32 = 0.0302 so this works.

For triangle C, Angle x = 145 and sin(145)/32 = 0.0179 so not possible.

For Triangle D. Angle x = 0.0311 so not quite possible.

For Triangle E, Angle x = 0.0302 so this is possible as well