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18 February, 04:47

One of the acute angles of a right triangle is 50 ° and its hypotenuse is 7 inches. find the lengths of its legs to the nearest tenth of an inch.

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  1. 18 February, 07:24
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    In a right triangle:

    the sine of an angle * length (the hypotenuse) = length (opposite leg)

    the cosine of that angle * length (the hypotenuse) = length (adjacent leg)

    Using a scientific calculator we find: sin50°=0.766; cos50° = 0.643

    thus, the legs are:

    |opp leg| = sin50° * 7 in = 0.766 * 7 in = 5.4 in

    |adj leg| = cos50° * 7 in = 0.643 * 7 in = 4.5 in

    Answer:

    5.4, 4.5
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