Maybe one way is that if you have sinx=y , where y is a number, find from the tables for which x you have y.
Then if you find x, find x/2 and from the tables again find sin(x/2)
Note that since 45 is in the first quadrant, 45/2 is also in the first quadrant.
We know that
This is a quadratic equation. In your situation, we have :
Solve for T, by remembering it's positive (because it's a square)
And then take its square root, by remembering that it must be positive (because x/2 is in the first quadrant)