In a 30°-60°-90° triangle, the length of the hypotenuse is 30. Find the length of the longer leg.

1 answer:

6 0

In a 30-60-90 triangle the side opposite the 30 degree angle is half the length of the hypotenuse.
The shorter leg is the side opposite the 30 degree angle, therefore
the shorter leg = 30/2 = 15

By the Pythagorean theorem
the longer leg = √(30² - 15²) = √(900-225) = √675 = 15√3 ≈ 25.98 units

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