Would the solution be S 80 degrees E only?

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

There is a triangle consisting of the sailboat starting point, the harbor, and sailboat current Opposite the 14 mile side is a 25° angle, so we can determine the angle opposite the 32 mile side by using the sin law.

sin 25°/14 = sin B/32.

Thus, B = sin^-1(32 sin 25°/14) = 75.0130160987648 or 180°- 75.0130160987648

Rounding to the nearest degree, we have 75° and 105°

Then, as the other angle is 25°, the third angle of the triangle is 80° or 50°

It is S 80° E and

S 50° E

Answer 2

Using the law of sines:

14/sin(25) = 32/sin(x)

sin(x) = 32sin(25)/14

x= 75°

So S10ºE or N80°E will reach the overturned sailboat.

Answer 3

Draw and label a diagram!

P represents the port

B represents the boat

H represents the harbor.

sin B / 32 = sin 25º / 14

sin B = 0.96598

B = 75.0130º

m∠PHB = 79,99

S 80º E