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23 May, 06:23

One leg of a right triangle is twice the length of the other leg. What is the cosine of the angle between the longer leg and the hypotenuse?

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  1. 23 May, 09:13
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    Let x denote the length of the shorter leg. Then the longer leg has length 2x. The hypotenuse of the triangle has length √ (x² + (2x) ²) = √5 x.

    The cosine of the angle formed by the longer leg and the hypotenuse is 2x / (√5 x) = 2/√5 = 2√5 / 5

    The cosine of the other acute angle is x / (&radc; 5 x) = 1/√5 = √5 / 5
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