Or Big brain explaination (MATH ALERT):

In a right triangle ABC, whose right angle is A, the tangent ratio of the angle B is the opposite leg over the adjacent leg.

tan B = opposite/adjacent

Expressing the sine and cosine functions of the angle B:

sin B = opposite/hypotenuse => opposite = hypotenuse\sin B*

cos B = adjacent/hypotenuse => adjacent = hypotenuse\cos B*

Re-writing the tangent ratio:

tan B = opposite/adjacent <= > tan B = hypotenuse\sin B/hypotenuse*cos B*

Reducing hypotenuse:

tan B = sin B/cos B

Therefore, in a right angle triangle, the tangent ratio of an angle, except the right angle, is: tan = sin / cos .