Installing a window casement operator (on a window that's never had one before)
The pivot point for your operator is going to be off-axis from your window's hinge line. Because of that, as your window opens and shut, the distance from any single point on your window to the operator's pivot will change, which means you can't have a fixed-length arm attached to a fixed point on the window.

You can handle this in two ways:

1) Use a split arm operator, where the swung arm has a second link connecting it to a fixed point on the window. That way the two arms will flex as the window opens and shuts, compensating for the changing distance

2) Use a straight arm operator, where the end of the swung arm slides in a channel on the widow as the window opens and shuts.

Choosing the length of the arm is just figuring out the geometry. Getting it right may be difficult without some trial and error; you may consider buying where you can return the unit if it's wrong.