#What is the value of x?

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A. 4

B. 4sqrt3

C. 8

D. 8sqrt3

1 Answer
May 26, 2017

4sqrt(3) = x, or B

Explanation:

In this one we know the angle and the hypotenuse, but we don't know the opposite side. So we need something to relate opposite to hypotenuse when given a certain angle.

sin(theta) = "opposite"/"hypotenuse" Works well here.

In this case we need to plug everything in as we see it. theta is 60 degrees, opposite is the opposite leg from the angle or x, and hypotenuse is the longest side to the triangle or 8 in this case.
So:

sin(60) = x/8 Multiply 8 on both sides to isolate x
color(red)(8)sin(60) = (x*color(red)(8))/8
8sin(60) = x Now we just evaluate to get what x is equal to
(8sqrt(3))/2 = x
4sqrt(3) = x

So B is the answer