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Given two angles and the hypotenuse of a right triangle, when trying to find the length of the side opposite the given angle, why and how does it's angle and supplementary angle yield the same answer?

For example. Right triangle

hypotenuse = 5

angle = 77

opposite side = sine (77) * 5 = 4.87185032

supplementary angle of 77 = 103

opposite side = sine (103) * 5 = 4.87185032

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  • $\begingroup$ This holds for all $x$: $\sin x = \sin (180-x)$; (btw. in a right angled triangle the two other angles are complementary, i.e. they sum up to 90°) $\endgroup$ – coproc Sep 5 '15 at 22:08

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