Question

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

Answer 1

Answer:

$x=12,\\y=6\sqrt{3}$

Step-by-step explanation:

In all 30-60-90 triangles, the side lengths are in ratio $x:x\sqrt{3}:2x$, 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 $x:x\sqrt{3}:2x$.

Thus, we have:

$y=\boxed{6\sqrt{3}},\\x=2\cdot 6=\boxed{12}$