30.60.90. right triangle. How do I solve if the long leg is 10?

I dont have the short leg or hypotenuse

1 Answer
May 1, 2018

The short leg is (10sqrt3)/3, the hypotenuse is (20sqrt3)/3

Explanation:

The 30.60.90 law states that for any given right triangle with angles measuring 30 and 60 degrees:

The 30 degree angle's opposite side is x
The 60 degree angle's opposite side is xsqrt3
The 90 degree angle's opposite side is 2x

QuoraQuora

The "long leg" must be the 60 degree angle, so it is xsqrt3, or 10.
The short leg is thus (xsqrt3)/sqrt 3, or x, or simply, 10/sqrt3.
Based on that, the hypotenuse is 2x, or 20/sqrt3

We also need to rationalize the values.

10/sqrt3 * sqrt3/sqrt3 = (10sqrt3)/3

20/sqrt3 * sqrt3/sqrt3 = (20sqrt3)/3