Math

A 25-foot ladder stands against a vertical wall at an angle of n degrees with the ground. If sin n = 4 / 5, how far is the base of the ladder from the wall?
A. 12
B. 13
C. 14
D. 15
E. 16

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  1. Sin n = 4 / 5. Remember that the formula for sin would be Opposite / Hypotenuse. So:

    Sin n = Opposite / Hypotenuse = 4 / 5
    Sine n = Opposite / 25 = 4 / 5
    5 Opposite = 100
    5 / 5 Opposite = 100 / 5
    Opposite = 20.

    Now what we do is use Pythagorean Theorem to find the length of the adjacent side.

    a^2 + b^2 = c^2
    20^2 + b^2 = 25^2
    400 + b^2 = 625
    400 - 400 + b^2 = 625 - 400
    b^2 = 225
    sqrt(b^2) = sqrt(225)
    b = 15.
    Answer choice D

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    posted by Neil

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