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
1 answer:
Answer:
Correct answer: 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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where
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h is the height of the pyramid
in this problem we have that
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where
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so
substitute in the formula of volume
therefore
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