Excalibur0126
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Two lighthouses are located 40 miles from each other. A boat is spotted at an angle of 37 degrees northeast of the western lighthouse. At this point, the boat is 28 miles from the eastern lighthouse. How far is the boat from the western lighthouse?

A. 46.27 miles
B. 17.43 miles
C. Either 46.27 miles or 17.43 miles
D. There is no possible solution.

Respuesta :

jushmk
The arrangement of the Eastern and Western lighthouses and the position of the boat are as shown in the attached diagram.

Using sine rule,
28/Sin 37 = 40/Sin B => Sin B = (40 Sin 37)/28 = 0.8597 => B = Sin ^-1(0.8597) = 59.287°
Therefore,
Angle E = 180 - (37+59.287) = 83.713°

Using the sine rule again;
BW/Sin E = 28/Sin 37 => BW = (28 Sin 83.713)/Sin 37 = 46.246 ≈ 46.27 miles.

The boat is 46.27 miles from the western lighthouse. The correct answer is A.
Ver imagen jushmk

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