Question

Someone please explain this to me?

Answer 1

C.

Explanation:

When given a right triangle (a triangle with a `90` -degree angle) and a second angle measuring either `30^o, 60^o`, you have a `30-60-90` triangle.

`30-60-90` triangles are really nice because if you know one side, you can actually determine all of the sides.

The side opposite to the right angle is the largest; represented by `2a` where `a` would be the smallest side.

The side opposite to the `60^o` angle, in this case, side `x,` is represented by `sqrt(3)a`, where `a` would be the smallest side.

And finally, the side opposite to the `30^o` angle, in this case angle `C,` is `a,` the smallest side.

So, if `2a=12, a=12/2=6`, `x=asqrt(3)=6sqrt(3)`

C. is correct.

Here is the `30-60-90` triangle, for reference.