Solving the angles of a right triangle can be easy when two of them are already known. Since all of them add to 180 degrees, it’s a matter of subtracting the two known angles from 180 to find the third. When the only known angle is the 90 degree angle, but the lengths of the sides are known, it’s still possible to find the angles. In these cases, it’s necessary to use the trig ratios to find the remaining angles.

Anatomy of a Right Triangle

Any right triangle is going to have three sides and three angles. One of the angles is going to be 90 degrees and the remaining two angles will add up to 90 degrees, with 180 degrees in total. With right triangles, the side directly across from the right angle is the hypotenuse. For either of the other angles, there is an opposite side and an adjacent side.

The Six Trig Ratios

With a right triangle, there are six possible ratios to use depending on which angle is being solved. Each ratio involves a trig function and two of the sides to determine what the angle is. Only one ratio needs to be used for each triangle, as that will mean two angles are known and it’s easy to find the third. The six trig ratios are:

Sin = opposite/hypotenuse

Csc = 1/sin = hypotenuse/opposite