Question

The hypotenuse of a 30°-60°-90° triangle measures 6/3 inches . What is the length of the longer leg?

Answer 1

`sqrt3" in"`

Explanation:

In a `30-60-90` special right triangle:

Side opposite to `30` degrees: `x`
Side opposite to `60` degrees: `xsqrt3`
Side opposite to `90` degrees: `2x`

So, in this case, we must find the side opposite to the `60` degrees, because the hypotenuse (given in the question) is always the opposite side of `90` degrees, and the shortest side is always opposite to the shortest angle (in this case, `30` degrees).

First, we can use the given hypotenuse value and the expressions above to solve for `x`, the shortest leg length.

`2x= 2 " in"`

`x= 1 " in"`

Therefore, the longer leg:

`xsqrt3= sqrt3 " in"`