Question

What is the value of x in the triangle

Answer 1

7

Explanation:

In an 30-60-90 right triangle, the longer leg is the shorter leg multiplied by
`√(3)`

So
`7√(3) =x*\sqrt{3`

`7=x`

x=7

Answer 2

A. 21

Explanation:

This is a 30-60-90 triangle, where you have one 30° angle, one 60°, and one 90° (aka right) angle.

The sides of a 30-60-90 triangle adhere to the following rules:

• The side opposite the 30° angle is the shortest side and we can call its length "x".
• The side opposite the 60° angle is the medium length side and its length is given by x * √3. This means its length is the product of the length of the side opposite the 30° angle and √3.
• The side opposite the 90° (right) angle is the longest side (aka the hypotenuse) and its length is given by 2x. This means its length is twice the length of the side opposite the 30° angle.

Since 7√3 is the length of the side opposite the 30° angle, the entire expression represents x.

Since the length of the side opposite the 60° angle is given by x * √3, the length of this side is (7√3)(√3).

Simplifying gives us 7*3, which is 21.

Thus, the value of x in the triangle is 21 (answer choice A.)