From the top of the Cape San Juan Lighthouse, a 45 foot tall lighthouse located in Fajardo, Puerto rico, a tourist sights two boats coming into the coastline, one behind the other. The angle of depression to one boat is 21° and the angle of depression to the other boat is 40°. How far apart are the two boats?

Please show work

The correct answer is 7.54 foot apart.

Step-by-step explanation:

The height of the Cap San Juan Lighthouse is 45 foot.

The angle of depression of the first boat is given to be 40°.

Distance between the first boat and the lighthouse is cos 40° × 45 = 34.47 foot.

The angle of depression of second boat is given to be 21°.

Distance between the second boat and the lighthouse is cos 21° × 45 = 42.01 foot.

Therefore the boats are 42.01 - 34.47 = 7.54 foot apart from each other.

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