Does the cosine ratio apply to any triangle

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.

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