Solving right triangles is extremely straightforward! All you need is to keep a few relationships in your toolbelt.

Notice in the last three examples that the triangle has been relabeled. These correspond the following:

It's important to understand that if we look at the triangle from the point of view of a different angle, the legs A and O interchange:

**H = Hypotenuse**(the longest leg of the right triangle, opposite the 90 degree angle)**A = Adjacent Leg**(this is the leg that emits from the angle you're referring to)**O = Opposite Leg**(as it sounds, this is the leg found opposite the angle you're referring to)It's important to understand that if we look at the triangle from the point of view of a different angle, the legs A and O interchange:

Alright let's give it a shot.First, find the missing leg length with the Pythagorean Theorem. \[ x^2+12^2=13^2 \Longrightarrow x = 5 \] Now, we are given (from the perspective of the angle \( \theta \)) the adjacent leg (12) and the hypotenuse (13). We know from our relations above that \( \cos{\theta}=\frac{12}{13} \) so we can take the inverse cosine function of both sides and obtain \( \theta = 22.62^\circ \) Since the interior angles in all triangles sum to 180 degrees, to find the final angle, all we have to do is subtract the two known angles from 180. \( 180-90-22.62 = 67.38^\circ \) |