Question

the shorter leg of a 30-60-90 is 6. what is the length of the other leg?

Answer 1

6sqrt(3)

Answer 2

Well, the hypotenuse of this triangle would be twice the length of the shortest leg by the law of sines. sin(90)/x=sin(30)/6, so x=12. The other leg of the triangle would be equal to the short leg multiplied by sqrt(3) also by the law of sines. Sin(30)/6=sin(60)/x, so x=6sqrt(3).

Answer 3

30-60-90 triangle has the ratio of length which is 1-sqrt(3)-2.