trigonometry help please?

here is the question, i have tried it a few times but i cant figure out the right answer, help please:

An observer, whose eyes are 1.77 m above the ground, is standing 27.0 m away from a tree. The ground is level, and the tree is growing perpendicular to it. The observer's line of sight with the treetop makes an angle of 17.0° above the horizontal. How tall is the tree?

1 Answer

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  • 1 decade ago
    Best Answer

    Let:

    AB be the tree (A at the top, B on the ground),

    CD be the observer (C eye level, D ground),

    CE be a horizontal line with E on the tree.

    In triangle AEC, angle AEC = 90 deg, angle AEC = 17 deg.

    EC = 27.0 m.

    AE / EC = tan(AEC)

    AE = EC tan(AEC)

    = 27.0 tan(17).

    The height of the tree is:

    AB = AE + EB

    = AE + CD

    = 27.0 tan(17) + 1.77

    = 10.0 m.

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