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1 year ago

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An observer from the top of a lighthouse 370 feet above sea level sees two sailboats in the water. The angles of depression to t

he boats are 12 degrees and 10 degrees. How far apart are the boats, to the nearest foot?

1 answer:

noname [10]1 year ago

5 0

Answer:the sailboats are 358 feet apart.

Step-by-step explanation:

The diagram of the triangle representing the situation is shown in the attached photo.

B represents the position of the lighthouse.

D represents the position of the first sailboat.

C represents the position of the second sailboat.

x represents the distance between the two sailboats

We would apply trigonometric ratio

Tan # = opposite/adjacent

For triangle ABD,

Tan 12 = 370/AD

AD = 370/Tan 12 = 370/0.2126 = 1740.357 feet

For triangle ABC,

Tan 10 = 370/AC

AD = 370/Tan 10 = 370/0.1763 = 2098.695 feet

x = AC - AD = 2098.695 - 1740.357 = 358 feet

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