Question

find the value of each variable.
$x = \square$ and $y = \square$
(simplify your answers. type exact answers, using radicals as needed.)

Explanation:

Step1: Identify triangle type

This is a 30-60-90 right triangle, hypotenuse = 36.

Step2: Solve for x (opposite 30°)

In 30-60-90 triangles, side opposite 30° is $\frac{1}{2}$ hypotenuse.
$x = \frac{1}{2} \times 36 = 18$

Step3: Solve for y (adjacent to 30°)

Use Pythagorean theorem: $y = \sqrt{36^2 - x^2}$
$y = \sqrt{1296 - 324} = \sqrt{972} = 18\sqrt{3}$

Answer:

$x = 18$ and $y = 18\sqrt{3}$