Question

Use the ratio of a 30-60-90 triangle to solve for the variables.​

Answer 1

`x=12,\\y=6√(3)`

Explanation:

In all 30-60-90 triangles, the side lengths are in ratio
`x:x√(3):2x`, where
`x` is the side opposite to the 30 degree angle and
`2x` is the hypotenuse, or longest side, of the triangle.

Since there are 180 degrees in a triangle, the angle on top must be 30 degrees. Therefore, its opposite side is 6 and
`x=6` in the ratio
`x:x√(3):2x`.

Thus, we have:

`y=\boxed{6√(3)},\\x=2\cdot 6=\boxed{12}`