Question

Help me solve for x and y

Answer 1

Let's start his with some trigonometry
Cos60=x/30
X=15
Now we can use Pythagorean therom
15^2+b^2=30^2
B(y)= 25.98

Answer 2

In a 30-60-90 triangle, the shorter side is represented as $s$, the hypotenuse as $2s$, and the longer side as $s \sqrt{3}$.  Since we are given the hypotenuse's length, we can use it to solve for $s$:

$2s = 30 \\ s = 15$

We now have the value of the shorter side, or $x$ in your diagram - 15 units.  Next, we can use $s$ to solve for the long side's length:

$s \sqrt{3} = y \\ 15 \sqrt{3} = y$

The length of the longer side, $y$, is $15 \sqrt{3}$ (approxiamtely 26) units.