SOLUTION: In triangle ABC, angle A=30� and angle C=90�. If the length of BC is five more than one-fourth of AB, find the length of the longer leg of the triangle.

Question 1009190: In triangle ABC, angle A=30� and angle C=90�. If the length of BC is five more than one-fourth of AB, find the length of the longer leg of the triangle.
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
In such a 30-60-90 right triangle, the side opposite the 30 degree angle is half the hypotenuse. That side is BC here. So if we call the hypotenuse AB, x, then
(1/4)x + 5 = (1/2)x
5 = (1/4)x
x = 20 = AB
BC = 10 and
AC, the longer leg, is 10*sqrt(3).

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