Question

find the values of x and y. write your answers in simplest form.
x =
y =

Explanation:

Step1: Identify Triangle Type

The triangle is a 30 - 60 - 90 right triangle (right angle and one angle 60°). In a 30 - 60 - 90 triangle, the sides are in the ratio $1:\sqrt{3}:2$, where the side opposite 30° is the shortest, opposite 60° is $\sqrt{3}$ times the shortest, and hypotenuse is twice the shortest. Here, hypotenuse is 24, so the side opposite 30° (let's say $y$) is half the hypotenuse.
$y=\frac{24}{2}=12$

Step2: Find the Other Leg

The side opposite 60° (x) is $\sqrt{3}$ times the side opposite 30° (y). So $x = y\sqrt{3}=12\sqrt{3}$

Answer:

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