Answer: x=10√3, y=10
Explanation:
This is a 30-60-90 triangle. It is a special right triangle. We know that the hypotenuse length is 2x. The length of the leg opposite of 60° is x√3. The length of the leg opposite 30° is x. In all of these lengths, x applies to all of them. This means whatever x is, you would plug them into x to get the length.
Since we know the hypotenuse is 20, we can set it equal to 2x to find the value of x.
20=2x [Divide both sides by 2]
x=10
Now that we know x is 10, we can directly plug them into the established lengths above to find x and y on the triangle.
X is directly across from 60°. That means the length is x√3. Since x=10, we can plug it in.
10√3
Since y is directly across from 30°, the length of y is x. X=10, therefore, y=10.