What is the value of x?

60-30-15 Right Triangle

a. 15√3
b. 15/2
c. 5√3
d. 15√2/2

1 answer

The answer is option D.

In a 60-30-15 triangle, the side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is √3/2 times the length of the hypotenuse.

Given that the hypotenuse is 30, we can find the lengths of the other sides:

- Side opposite 30-degree angle: 30/2 = 15
- Side opposite 60-degree angle: (√3/2) x 30 = 15√3

Using the Pythagorean Theorem, we can find the length of the remaining side (x):

x^2 = (15√3)^2 - 15^2

x^2 = 675

x = 15√3/√2

x = 15√2/2

Therefore, the value of x is 15√2/2, which is option D.