Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? round to the nearest degree.

In the right triangle, the longest side is the hypotenuse.
Let α be the angle opposite to the side with a length of 12 units, then according to the Law of sines:



In a triangle, the three interior angles always add to 180° ⇒

third angle = 180 - 90 - 67 = 23°


67° and 23°  (to the nearest degree).