SOLUTION: The sum of the measures of the legs of a right triangle is 48. The tangent of one of the acute angles is 1/5. What is the measure of the longer leg?

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Question 268063: The sum of the measures of the legs of a right triangle is 48. The tangent of one of the acute angles is 1/5. What is the measure of the longer leg?
Answer by CharlesG2(834) About Me  (Show Source):
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The sum of the measures of the legs of a right triangle is 48. The tangent of one of the acute angles is 1/5. What is the measure of the longer leg?
tangent is opposite/adjacent is 1/5
1/5 = x/(48-x)
1 = 5x/(48-x)
48-x = 5x
48 = 6x
8 = x
48 - 8 = 40 which is the measure of the longer leg
8/40 = 1/5 = opposite/adjacent = tangent of one of the acute angles