Question

Find the value of x and the value of y.

Answer 1

Answer:

Option C.

$x=2\sqrt{2}$

$y=2\sqrt{6}$

Step-by-step explanation:

step 1

Find the value of x

In the right triangle of the figure

$sin(30\°)=\frac{x}{4\sqrt{2}}$ -----> opposite side angle of 30 degrees divided by the hypotenuse

Remember that

$sin(30\°)=\frac{1}{2}$

so

$\frac{1}{2}=\frac{x}{4\sqrt{2}}$

$x=\frac{4\sqrt{2}}{2}$

$x=2\sqrt{2}$

step 2

Find the value of y

In the right triangle of the figure

$cos(30\°)=\frac{y}{4\sqrt{2}}$ -----> adjacent side angle of 30 degrees divided by the hypotenuse

Remember that

$cos(30\°)=\frac{\sqrt{3}}{2}$

so

$\frac{\sqrt{3}}{2}=\frac{y}{4\sqrt{2}}$

$y=\frac{4\sqrt{6}}{2}$

$y=2\sqrt{6}$