i have no idea how to set up an equation to solve for a right triangle where i am supposed to find the hypotenuse (x) after being given all

The problem here is that we don't know which angle is opposite the side with the length of 10.....is it the 70° angle or the 20° angle ???

First, let us assume it is the 70° angle....by the Law of Sines, we have

x/sin90  = 10/sin70   and x = about 10.64  = the hypotenuse length

And the other leg (L) is just

10/sin70 = L / sin 20   →   L =   10sin20/sin70 = about 3.64

Check   (3.64)^2 + 10^2 =  10.64^2  ??   ...if you evalute this on a calculator, you will see that it is approximately true

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But.....what it the side of 10 is opposite the 20° angle??  .....again, using the Law of Sines we have

x/sin90 = 10/sin 20   and x = about 29.238 =  the hypotetnuse length

And the other leg L is given by:

10/sin20 = L/sin70   →  L = 10sin70/sin20 = about 27.475

Check  (27.475)^2 + 10^2 = 29.238^2 ????   and agian, this is approximately true........

So....we have two possible right triangles depending upon the orientation of the sides and angles