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Can the opposite in a trig ratio also be a hypotenuse?

In the problem where there is a triangle ABC and with AB being 12, BC being 9, and AC being 15, we are asked to find the angle measure of A.

I know that you can prove it with the Pythagorean theorem because 144+81=225, but I tried using the trig ratio

sin-1 = 15/15 which gets you 90...

I've only tried this with this case, but does this apply to all problems?

Thanks

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    `sin-1 = 15/15 which gets you 90` This will get you `90` regardless of the lengths of the two other sides. But *not* all triangles with $AC=15$ are *right* triangles. – 2017-01-23

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