Question

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

I dont have the short leg or hypotenuse

Answer 1

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`

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`