Question

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

x = 22, y = 11
`√(3)`
x = 11, y = 22
`√(3)`
x = 22
`√(3)`, y = 11
x = 11
`√(3)`, y = 22

Answer 1

D

Explanation:

Since this is a right triangle, and we are given that one of the other angles is 30°, we have a 30°, 60°, 90° triangle.

In a 30°, 60°, 90° triangle, the side lengths are all related as shown below.

We should determine a first. a is the measure of the side opposite to the 30° angle. Thus:

`a=11`

The side opposite to the 60° angle is given by a√3. Since a = 11, the side opposite to the 60° angle or x is:

`x=(11)√(3)=11\sqrt3`

Finally, the hypotenuse will be 2a. Since a = 11, the hypotenuse or y will be:

`y=2(11)=22`

Hence, x = 11√3 and y = 22.

Our answer is D.