Geometry

at 10 feet away from the base of a tree, angle the top of a tree males with the ground is 61 degrees. of the tree grows at an angle of 78 degress with the respect to the ground, how tall is the tree to the nearest foot?

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  1. If the point directly below the top of the tree is x feet from the base, then we have

    h/(x+10) = tan61°
    h/x = tan78°
    eliminating x, we get the height

    h/tan61° - 10 = h/tan78°
    h = 10(cot61°-cot78°)

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