Carl spies a potential Sasquatch nest at a bearing of N12Â°E and radios Jeff, who is at a bearing of N49Â°E from Carl's position. From Jeff's position, the nest is at a bearing of S70Â°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.

Question

Isaiah

Mathematics

18 November, 19:36

Carl spies a potential Sasquatch nest at a bearing of N12Â°E and radios Jeff, who is at a bearing of N49Â°E from Carl's position. From Jeff's position, the nest is at a bearing of S70Â°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.

+2

Answers (1)

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Chance · Answer 1

JS = 344 ft

Step-by-step 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