March 28, 2017

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a tree grew at a 3 degree slant from the vertical. at a point 60 feet from the tree, the angle of elevation to the top of the tree is 14 degrees. find the height of the tree to the nearest tenth of a foot.

  • geometry - ,

    Depends if the tree is leaning 3° towards the observer or away from the observer.

    I will assume "towards"
    So the diagram will show a triangle with two base angles of 87° and 14° with the contained side of 60 ft
    leaving the vertical angle at the top 79°
    by sine law:
    x/sin14 = 60/sin79
    x = 60sin14/sin79 = appr 14.8

    If you had the other option, repeat with the base angle of 93° instead of 87

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