Question

Find the value of x. Write your answer in simplest form.

Answer 1

x = 4

Explanation:

Using the sine ratio in the right triangle and the exact value

sin60° =
`(√(3) )/(2)` , then

sin60° =
`(opposite)/(hypotenuse)` =
`(2√(3) )/(x)` =
`(√(3) )/(2)` ( cross- multiply )

`√(3)` x = 4
`√(3)` ( divide both sides by
`√(3)` )

x = 4

Answer 2

It would be 4.

Explanation:

Alright, this is a 30-60-90 special triangle. With special triangles, there is a formula that you can use to find unknown side lengths of a triangle if you know the angles of it.

With a 30-60-90 triangle, the sides opposite of these angles are:

30 degrees : x

60 degrees: x√3

90 degrees: 2x

With this, we can see that opposite of the 60 degrees is the length 2√3. From this, it can be found that the opposite of the 30 degrees would be 2, given the formula of the special triangle. Lastly, the unknown value would be 4, since it is two times this amount.