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25 April, 06:04

An 85-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground. How high is the top of the tree house? Round your answer to the nearest tenth of a foot.

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  1. 25 April, 06:23
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    For this case we can model the problem as a rectangle triangle.

    We have the hypotenuse and the angle.

    We want to find the height.

    For this, we use the following trigonometric relationship:

    sine (x) = C. O / h

    Where,

    x: angle

    C. O: opposite leg

    h: hypotenuse

    Clearing C. O we have:

    C. O = 85 * sine (45)

    C. O = 60.1040764

    Round to the nearest tenth of a foot:

    C. O = 60 feet

    Answer:

    the top of the tree house is 60 feet high
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