Alg/Trig

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The angle of elevation from a point on the ground to the top of a tree is 39.8 degrees. The angle of elevation from a point 51.7 ft farther back to the top of the tree is 19.7 degrees. Help find the height of the tree.

  • Alg/Trig -

    well, you know that

    h/x = tan 39.8°
    h/(x+51.7) = tan 19.7°

    Now eliminate x and solve for h:

    h/tan39.8° = h/tan19.7° - 51.7
    1.2h = 2.8h - 51.7
    h = 32.3

    check my math, but that's the method to my madness.

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