Which solution finds the value of x in the triangle below? !

8 is the hypotenuse and x is the adjacent side to the 60-degree angle. This means that you would need cosine (adjacent over hypotenuse) or secant (hypotenuse over adjacent). Cosine is not an option so it's secant.

sec 60 degrees = 8/x

Next, in a 30 60 90 triangle, you know that the side lengths are 1, 1/2 and sqrt(3)/2. So the secant of 60 degrees is 1 divided by 1/2 which is 2. 

So the answer is the first question: x = 4

We have the angle of 60°
x is the adjacent leg to the angle of 60°
and 8 is the hypothenuse
Then we must use a function that relates the adjacent leg with the hypothenuse. We have two options: cosine or secant. We don't have in the options cosine, then we must use secant.

sec 60°= hypothenuse / Adjacent leg
sec 60"=8 / x; sec 60°=2
2=8 / x
2x=8
x=4

First option