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17 July, 11:07

Given that the hypotenuse of this right triangle is 25 cm long and that tan (θ) = 3find the values of x and y, accurate to the nearest tenth.

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  1. 17 July, 11:27
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    The tangent of an angle is the opposite side divided by the adjacent side of the triangle, relative to the angle. By tan theta = 3, it means that, the adjacent side is thrice as long as the opposite side.

    3a = o

    Then, using Pythagorean's theorem:

    25² = a² + o²

    Substituting o,

    25² = a² + (3a) ²

    25² = a² + 9a²

    25² = 10a²

    a = 7.9 cm

    Then, 3 (7.9) = o = 23.7 cm

    So, the opposite side is 23.7 cm and the adjacent side is 7.9 cm.
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