DoglovingJim wrote:How would one go about figuring out the length for the hypotenuse in this?

In my mind the formula should be to combine the opposite and the adjacent (using Tan) and find the square route of what they equal combined and that would be the length of x. But since I'm lacking the length of the adjacent I have no clue what to do, and in my head the multiple choice answers don't make sense.

I wonder what's the formula for when you only have the length of one side and an angle?

Forget Pythagoras here. Pythagoras links the three side lengths, and the length of one side is irrelevant to you.

You want basic trigonometry here: that links an angle and two side lengths. You generally need to know two of them and want to find a third. It doesn't matter which two: if you know two side lengths you can find an angle, and if you know a length and an angle you can find another length.

You have an angle (30°), one side length (Adjacent to that angle -5 units), and want another side length (hypotenuse - x).

There's three basic trig functions, tangent, cosine, and sine. Tan is not the one you want here, since Opposite (the base of the triangle - remember, we're working with the top angle, not θ) is neither known nor wanted.

SOH CAH TOA:

So with Adjacent and Hypotenuse, we want cosine.

Of course, we can easily find the angle θ by subtracting the other two angles from 180°, so we could have used that, and sine, to find the hypotenuse. That would give us a very similar answer, because

sin(90°-θ) = cos(θ).

Also, not that anyone minds you asking in here I'm sure. It's not as though it can really be off-topic. But if you'd rather, we have a

maths thread