Question

What is the value of x?

Answer 1

Answer: 4

Step-by-step explanation:

Well, first you need to use the 30-60-90 special triangle property to find out the length of the hypotenuse triangle with the side with the length 2√3.

The 30-60-90 property states that if the hypotenuse is x, then the leg opposite to 30 degrees has the length of x/2 and the leg opposite to 60 degrees has the length of (x√3)/2. So if the leg opposite to 60 degrees has a length of 2√3, the hypotenuse can be found with this equation: 2√3=(x√3)/2, and when you solve this equation, you should get x=4.

Now that you have figured out the hyptenuse of the 30-60-90 triangle, you can use that leg to find the length of the other leg in the 45-45-90 triangle. Since both of the legs are opposite to the same degree angle, they are both congruent, and the value of x in the problem is 4.