Question

How do i solve for y and x?

Answer 1

Use the 30-60-90 rule

X= 18 and y=6sqrt3

Answer 2

You use the facts about a 30, 60, 90 triangle.

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
`√(3)`

We know the side opposite the 90 degree angle.

2a = 12
`√(3)`

Divide by 2.

a=6
`√(3)`

a is the side opposite the 30 degree angle (y)

Because we know a, we can find a
`√(3)`.

6
`√(3 ) (√(3))`

The square roots cancel, leaving 3.

6 times 3 is 18.

Therefore, the side opposite the 60 degree angle (x) is 18.