Question

PLEASE ANSWER AS SOON AS POSSIBLE WILL GIVE "Brainliest" TO THE FIRST CORRECT PERSON!!!

Answer 1

Answer: $x=18$ ; $y=6\sqrt{3}$

Step-by-step explanation:

You can write two expressions that are in terms of 'x' and 'y'. This is a right triangle, so Pythagorean's theorem can be used. We can also use the angle to find the sine of 30 degrees.

Pythagorean's Theorem:

The values 'a' and 'b' are the two shorter sides of the triangle, while the value 'c' is the longest side of the triangle; the hypotenuse.

$a^2+b^2=c^2$

$x^2+y^2=(12\sqrt{3} )^2$

$x^2+y^2=12^2*\sqrt{3} ^2=432$

Sine of the Angle:

Sine is defined to be the opposite side divided by the hypotenuse. Let's take the sine of 30 degrees:

$sin(\alpha )=opposite/hypotenuse$

$sin(30)=y/12\sqrt{3}$

$\frac{1}{2} =y/12\sqrt{3}$

$y=6\sqrt{3}$

Plug this value of 'y' into the first expression derived from Pythagorean's theorem:

$x^2+y^2=432$

$x^2+(6\sqrt{3} )^2=432$

$x^2+108=432$

$x^2=432-108=324$

$x=\sqrt{324}$

$x=18$

Use this value of 'x' to solve for 'y' in the expression from Pythagorean's theorem:

$(\sqrt{324})^2+y^2=432$

$324+y^2=432$

$y^2=432-324=108$

$y=\sqrt{108}$

$y=\sqrt{36*3}$

$y=6\sqrt{3}$