We can use properties of similar triangles to relate sines to right triangles. In the figure above the triangle ABC is a right triangle with a right angle at angle C and a hypotenuse of length 1. Consider a similar right triangle AB'C' with a hypotenuse of arbitrary length. (If your web browser is Java-enabled, you can drag the points B' to change the size of the right triangle AB'C'.)

Since the triangles are similar, the ratio BC to AB equals the ratio B'C' to AB'. But AB equals 1. Hence,
BC = B'C' / AB'
but BC = sin A, so
sin A = B'C' / AB'
This result is most easily remembered as the sine of an angle in a right triangle equals the opposite side divided by the hypotenuse: sin= opp/hyp.