Answer:
You use the facts about a 30, 60, 90 triangle.
Step-by-step explanation:
The angles in a triangle add up to 180.
90+30+x=180
120+x=180
x=60
This is a 30-60-90 right triangle.
The side opposite the 30 degree angle is a.
The side opposite the 90 degree angle (hypotenuse) is 2a.
The side opposite the 60 degree angle is a[tex]\sqrt{3}[/tex]
We know the side opposite the 90 degree angle.
2a = 12[tex]\sqrt{3}[/tex]
Divide by 2.
a=6[tex]\sqrt{3}[/tex]
a is the side opposite the 30 degree angle (y)
Because we know a, we can find a[tex]\sqrt{3}[/tex].
6[tex]\sqrt{3 } (\sqrt{3})[/tex]
The square roots cancel, leaving 3.
6 times 3 is 18.
Therefore, the side opposite the 60 degree angle (x) is 18.
