The angle of depression from the top of a lighthouse to a boat is 27*. if the direct distance from the top of lighthouse to the boat is 462 ft, find the distance from the base of the lighthouse to the boat

Correct  Db = 411 .18 ft

Step-by-step explanation:

Given:

α = 27°  angle of depression

Dt = 462 ft  distance from the top of lighthouse to the boat

Db = ?   distance from the base of the lighthouse to the boat

Here we have a right triangle with hypotenuse Dt and one leg Db.

By definition

cos α = Db / Dt  ⇒ Db = Dt · cos α

Db = 462 · cos 27° = 462 · 0.89 = 411 .18 ft

Db = 411 .18 ft

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0 is its x and y coordinate