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March 29, 2017

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From a point on the ground 25 ft. from the foot of the tree, the angle of elevation of the top of the tree is 32 degrees. How do you find the height of the tree to the nearest foot?

  • Pre-Calculus - ,

    The tree height is 25 tan32 = 15.6 feet
    To the nearest foot, that would be 16.

    I assume you are familiar with the tangent of an angle.

  • Pre-Calculus - ,

    It'll help you sove this if you draw a picture.(Not the greatest below but you get the idea)
    .|
    . |
    . |
    . |x
    . |
    ._____________|
    25ft

    The 32 degrees should go in the bottom left corner of the triangle. To solve for x, you would use tangent. The problem would be set up as tan(32)=x/25
    Then, mulitply both sides by 25 to get x by itself so you have:
    25tan(32)=x
    When you plug this into a calculator, you get 16.525, so the tree is about 17ft tall

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