Say the angle A is the right angle of the triangle ABC.
The distances |AB|, |BC| and |CA| are usualy denoted by c, a and b.
Take point B in a suitable way as center of a trigonometric circle
Now sin(B),cos(B) and 1 are directly propertional with b, c and a.
sin(B) cos(B) 1 ------ = ------ = --- b c a => sin(B) = b/a cos(B) = c/a tan(B) = b/c and since the angles B and C are complementary angles cos(C) = b/a sin(C) = c/a tan(C) = c/b
In each right-angled triangle ABC, with A as right angle, we have
sin(B) = b/a cos(B) = c/a tan(B) = b/c cos(C) = b/a sin(C) = c/a tan(C) = c/b