The longer leg of a 30°-60°-90° triangle is 6. What is the length of the hypotenuse?
Question
The longer leg of a 30°-60°-90° triangle is 6. What is the length of the hypotenuse?
Solution
In a 30°-60°-90° triangle, the sides are in the ratio 1:√3:2. The longer leg is √3 times the length of the shorter leg, and the hypotenuse is twice the length of the shorter leg.
Given that the longer leg is 6, we can find the length of the shorter leg by dividing by √3.
So, the shorter leg = 6/√3 = 2√3.
Since the hypotenuse is twice the length of the shorter leg, the hypotenuse = 2 * 2√3 = 4√3.
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