SOLUTION: In a 30�- 60�- 90� right triangle, the shorter leg is 5 cm. How long are the other two sides of the triangle?

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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