The tangent ratio is the side opposite the reference angle over the side adjacent the reference angle. If you set up a right triangle in the first quadrant where both x and y are positive, the side opposite the reference angle is 8 and the stationary part of the angle is on the x axis as 5. We are now lacking the hypotenuse measure of this right triangle. Find it with Pythagorean's Theorem. c^2 - 8^2 + 5^2. c^2 = 64 + 25, so the length of the hypotenuse is sqrt 89. The cosine ratio is the side adjacent over the hypotenuse, so the cosine of that same angle is 5/sqrt89.
