Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the 30°-60°-90° Triangle Theorem to find the answer.
A right triangle is shown with an angle that measures 60 degrees. The leg adjacent to the 60 degree angle is labeled 5. The leg opposite of the 60 degree angle is labeled x. The hypotenuse is labeled y.
Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
(2 points)
To find the value of x, we can use the 30°-60°-90° Triangle Theorem, which states that in a right triangle with angles measuring 30°, 60°, and 90°, the side lengths are in a ratio of 1:√3:2.
In this case, we are given the leg adjacent to the 60 degree angle, which is 5. We can set up the ratio as follows:
5/x = √3/1
Cross multiply:
5 = x√3
Divide by √3 to solve for x:
x = 5/√3
To rationalize the denominator, multiply the numerator and denominator by √3:
x = (5√3) / (√3 * √3)
x = 5√3 / 3
Therefore, the value of x is 5√3 / 3.