It's called trigonometry - ya know - all that SOH CAH TOA CAO SHA CHO stuff from high school ?? (I'm assuming that they teach that in the US - I learned it in RSA).

In this case , the distance that you are looking for is opposite the deflection angle, so you want to find O ; use the hypotenuse (H) as your other distance.

So, you're working with theta (the angle), O (the distance that the control surface tip is from its neutral position, and H (the distance from the hinge centreline to the tip of the control surface, as measured in cross section).

Sin (Theta) = O / H

=> O = H * Sin (Theta)

Grab your pocket calculator and use the above - out pops the answer.

Gordon