How do you find an angle in a right-angled triangle when you are given two of its side's lengths?

You must first identify the names of the two sides in relation to the angle you are trying to find out. The technique "sohcahtoa" is generally very helpful in working this out. This abbreviation stands for:

Sine=Opposite/Hypotenuse

Cosine=Adjacent/Hypotenuse

Tangent=Opposite/Adjacent

Then to find the angle, you simply use the inverse of the function you have found you needed (found on your calculator) on the fraction and it should come out with the answer.