A a right triangle with a 60° angle is shown. The side across from the right angle is labeled 18 and the side next to the 60° angle is labeled x.

Question

Question
Use the triangle to answer the question.
Find the value of x in the triangle shown.
(1 point)
Responses

3
3

5
5

6
6

9

Answer 1

In a right triangle with one angle of 60°, the sides can be determined using the properties of a 30-60-90 triangle. The ratios of the sides in a 30-60-90 triangle are as follows:

• The side opposite the 30° angle is \(x\).
• The side opposite the 60° angle is \(x\sqrt{3}\).
• The hypotenuse is \(2x\).

In your case, the side opposite the right angle (the hypotenuse) is 18.

Using the hypotenuse: \[ 2x = 18 \]

To find \(x\): \[ x = \frac{18}{2} = 9 \]

Now, you also need to find the side next to the 60° angle (which is opposite the 30° angle). This side corresponds to the side opposite the 30° angle in the 30-60-90 triangle ratio, which is \(x\).

Therefore, we can conclude that:

• Side across from 60° (labeled \(x\)) = \(9\sqrt{3}\) (not what's being asked).
• Side next to the 60° angle (the answer you need) = \(x = 9\).

So the value of \(x\) is:

9