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[Originally posted in the Discussions]
Why is the shorter leg 3/2 and the longer leg 3/2 sqrt3? Is there some rule that I don't know?
In any 30-60-90 right triangle, the ratio of the side lengths is 1 : √ 3 : 2. So here, since we know the hypotenuse is 3, we can use the above fact to learn that the side lengths must be 3/2, 3√ 3/2 and 3. Hope that helps!