Solving right triangles simply means putting what you know to use in finding missing angles and sides in a triangle. Consider the following diagram, in which it is given that C = 90 degrees.
 

Sample #1
a = 10, b = 15.

Solution
A = tan^-1 (10/15) = 33.96 degrees
B = 90 - A = 56.31 degrees
c = ?(10² + 15²) = 18.03

Sample #2
a = 10, A = 30 degrees

Solution
B = 90 - A = 60
sin 30 = a / c, so c = 20
cos 30 = b / c, so b = 17.32

If you are given two sides, or an angle and a side, you can solve the triangle. If you are given only angles, you cannot solve the triangle.

For the problems below, use the diagram given on this page, and solve the triangles. Your answer will always consist of three pieces of information: two sides and an angle, or a side and two angles. If a problem can't be solved, explain why.