Label the angles and sides of the triangle with the dimensions that are given. To calculate the length of a triangle's side given an angle, you will need the length of one other side. If you are not given one angle and the length of at least one side, then the problem cannot be done.
Determine what side of the triangle (hypotenuse, opposite or adjacent side) you need to find. The hypotenuse is the longest side of a triangle. Depending on the angle given, label the opposite side across from the given angle and label the adjacent side as the one that lies next to the angle on either side.
Determine the appropriate trigonometric relationship to use to figure the length of a side of the triangle depending on the information already given. For example, if you have a triangle with an angle given at 53 degrees and a hypotenuse of 8 centimeters, then sine of 53 degrees would equal the opposite side / 8 cm. Use a calculator with trigonometric functions or a table of trigonometric function value to look up the sine of 53 degrees. Since the sine of 53 degrees is 0.80, cross-multiplying would yield 0.80 times 8 cm or 6.4 cm for the length of the opposite side.