A:
The angles in a triangle add up to 180 degrees.
If sum of two of the angles is equal to the third they must be 45, 45 and 90 degrees.
(To see this, try to make it work any other way).
In this right angled triangle let the unknown short side be x.
By Pythagoras x^2 +12^2 = 13^2
So x^2 = 169 - 144 = 25
x =5
Hope that helped,
Regards - Ian