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Trigonometry

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frrom outlook tower 80ft. high, a man observes from a position 6.5ft. below the top of the tower that the angle of elevstion of the top of certain tree is 12deg40mins and the angle of depression of its base is 72deg20mins. If the base of the tower and the base of the tree are at the same level, what is the height of the tree?

  • Trigonometry - ,

    The line of sight of the 72 deg angle
    is represented by the hyp. of a rt triangle. The ht. of the observer above
    the bottom of tree represents the ver.
    side of the triangle.The hor. side is
    the dist. from the tree to the bottom
    of tower.The line of sight of the 12
    deg. angle is the hyp of a 2nd rt.
    triangle. Its' hor. side is = to hor.
    side of 1st triangle.

    Tan(72,20min) = 73.5 / X,
    X = 73.5 / Tan(72,20min) = 23.41 Ft.
    = hor. dist. from tree to tower.

    Tan(12,40min) = Y / 23.41 ,
    Y = 23.41 * Tan(12,40min) = 5.26 Ft
    = ver. side of 2nd triangle.
    h = 73.5 - 5.26 = 68.2 Ft. = ht.
    of tree.

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