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29 December, 09:00

Carol is standing 8 feet from a lamppost. The angle of elevation from her eyes to the top of the lamppost is 20o, and the angle of depression from her eyes to the bottom of the post is 35o. How tall is the lamppost?

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  1. 29 December, 09:26
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    Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft

    Step-by-step explanation:

    The illustration form a triangle that can be demarcated into 2 right angle triangle. One triangle representing depression triangle and the other elevation triangle.

    Depression triangle

    The opposite side of the triangle formed is the length of the pole from the base to the horizontal line of sight. Therefore,

    using tangential ratio

    tan 35° = opposite/adjacent

    tan 35° = a/8

    cross multiply

    a = 8 tan 35°

    a = 8 * 0.70020753821

    a = 5.60166030568

    a = 5.602 ft

    Elevation triangle

    The opposite side of this right angle triangle represent the length from the horizontal line of sight to the top of the lamppost.

    tan 20° = opposite/adjacent

    tan 20° = b/8

    cross multiply

    b = 8 tan 20°

    b = 8 * 0.36397023426

    b = 2.91176187413

    b = 2.912 ft

    Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft
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