You will see the trig functions applied to all kinds of situations. The most familiar application(s) is the right triangle.
Here's an important non-right-triangle example:
Law of Cosines:
c^2 = a^2 + b^2 - 2ab*cos C.
Here C would generally NOT be a right angle, but could be either acute or obtuse. Note that if C = 90 deg here, the Law of Cosines takes on the form of the Pythagorean Theorem c^2 = a^2 + b^2.
