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16 February, 20:52

The angle of depression from a lighthouse to a boat in the water is 14° if the boat is 532 feet from the base of the light house what is the height of the lighthouse?

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  1. 16 February, 20:54
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    To solve this exercise, you must follow the proccedure below:

    1. You have:

    Tan (α) = Opposite/Adjacent

    α is the angle of depression (α=14°).

    Adjacent=532 feet

    Opposite=x

    2. When you substitute these values into Tan (α) = Opposite/Adjacent, you obtain:

    Tan (α) = Opposite/Adjacent

    Tan (14°) = x/532

    3. Now, you must clear "x", as below:

    x = (532) (Tan (14°))

    x=132.64 feet

    What is the height of the lighthouse?

    The answer is: The height of the house is 132.64 feet
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