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*
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 .