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3 years ago

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Ships A and B are 1,425 feet apart and detect a submarine below them. The angle of depression from ship A to the submarine is 59

°, and the angle of depression from ship B to the submarine is 47°. How far away is the submarine from the two ships? Round to the nearest hundredth of a foot. The distance from ship A to the submarine is about feet. The distance from ship B to the submarine is about feet.

2 answers:

andreyandreev [35.5K]3 years ago

4 0

Answer: The distance from ship B to the submarine is 1270.68 feet and the distance from ship A to the submarine is 1084.18 feet.

Step-by-step explanation:

Since we have given that

Distance between Ships A and B = 1425 feet

Angle of depression from ship A to the submarine =59°

Angle of depression from ship B to the submarine = 47°

As shown in the figure below:

Remaining angle will be

$180\textdegree-(47\textdegree+59\textdegree)\\\\=180\textdegree-106\textdegree\\\\=74\textdegree$

So, we will use "Sine formula ":

$\frac{\sin 74\textdegree}{1425}=\frac{\sin 59\textdegree}{B}\\\\B=\frac{1425\times \sin 59\textdegree}{\sin 74\textdegree}\\\\B=1270.68\ feet$

Similarly,

$\frac{\sin 74\textdegree}{1425}=\frac{\sin 47\textdegree}{A}\\\\A=\frac{1425\times \sin 47\textdegree}{\sin 74\textdegree}\\\\A=1084.18\ feet$

Hence, the distance from ship B to the submarine is 1270.68 feet and the distance from ship A to the submarine is 1084.18 feet.

andrey2020 [161]3 years ago

3 0

Answer:

For ship A to the submarine is 1084.18 feet. see attached image

Step-by-step explanation:

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