Question 287613: In a 30°- 60°- 90° right triangle, the shorter leg is 5 cm. How long are the other two sides of the triangle? Answer by CharlesG2(834) (Show Source):
You can put this solution on YOUR website! In a 30°- 60°- 90° right triangle, the shorter leg is 5 cm. How long are the other two sides of the triangle?
in 30°- 60°- 90° the sides are always in ratio 1:sqrt(3):2
sin 30° = opp/hyp = 1/2 = 5/hyp --> 1 * hyp = 2 * 5 --> hyp = 10
tan 30° = opp/adj = 1/x --> x * tan 30° = 1 --> x = 1/tan 30°
x = 1/tan 30° --> x = sqrt(3)
sides are 5 cm, 5sqrt(3) cm, and 10 cm
pythagorean theorem a^2 + b^2 = c^2 --> 5^2 + (5sqrt(3))^2 = 25 + (25*3) = 25 + 75 = 100 --> c = 10
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