Have you studied trigonometry at all?
If so, you have the standard trigonometric ratios to be used: sine and cosine.
If not, then you're probably out of your depth.
Okay, if you have a right triangle, the hypotenuse of which (side opposite the right angle) is 16 feet long, and the other angle is 68 degrees, how do you calculate the length of the opposite side? I have no idea how to go about finding this. Please help me.
It's just a little right triangle trigonometry.
Let's say the hypotenuse is labeled 'c'
One leg is labeled 'a' and the other leg is labeled 'b'
You know that one of the acute angles is 68 degrees. Let's say that it is the angle made with the hypotenuse and leg 'b'. See diagram.
Solve these equations for 'a' and 'b', respectively, and you have what you need.