Question

Definition: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 12 miles away from the nearest harbor, which is 28 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.

Answer 1

Answer:

S 75°E

S 55°E

Step-by-step explanation:

Take the law if sines of a triangle:

$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

Where,

a = 28 miles

B = 25°

b = 12 miles

First solve for A, using the law of sines:

$\frac{a}{sinA} = \frac{b}{sinB}$

$\frac{28}{sinA} = \frac{12}{sin25}$

Cross multiply:

$28 sin25 = 12 sinA$

$11.83 = 12 sinA$

$Sin A = \frac{11.83}{12}$

$Sin A = 0.986$

$A = sin^-^1(0.986)$

$A = 80.44 degrees$

Since A = 80.44° find A supplement, A`:

A` = 180 - 80.44

A` = 99.56°

If A` + B < 180°, find C.

Thus,

A` + B = 99.56 + 25 = 124.56

We can see that A` + B < 180

Find C:

C = 180 - (80.44+25) = 74.56° ≈ 75°

C` = 180 - (99.56+25) = 55.44° ≈ 55°

Rewrite in bearing form:

S 75°E

S 55°E