Question

Carl spies a potential Sasquatch nest at a bearing of N12°E and radios Jeff, who is at a bearing of N49°E from Carl's position. From Jeff's position, the nest is at a bearing of S70°W.

a. If Jeff and Carl are 500 feet apart, how far is Jeff from the Sasquatch nest? Round your answer to the nearest foot.

Answer 1

JS = 344 ft

Explanation:

Draw an imaginary triangle with

C on the left, J at upper right,

and S somewhere above the line CJ, but lower than J.

Then, interior angle at C = 49 - 12 = 37°

Also,The interior angle at J = 70 - 49 = 21°

So, the interior angle at S = 70 + 49 = 119°

Now, using the law of sines, we have;

JS / sin(37) = JC / sin(119)

Thus,

JS = (500 ft) (sin 37) / (sin 119)

JS = (500 x 0.6018)/0.8746

JS = 300.9/0.8746

JS = 344 ft