The Physics of the Ostrich Hat Attack

I took this picture of my sister and a dangerously close ostrich right next to her during our 2007 vacation in the Philippines. My family and I were visiting the famous Baluarte, a zoo in Vigan built by the Filipino politician Chavit Singson. We were walking back to the parking lot and on the way, we had to pass by a circular track where the ostriches were loose (there were employees there, of course, to keep a close eye on the ostriches and the visitors). My daring sister decided to stop and take a picture with an ostrich less than a foot away from her. Fortunately, the ostrich did not in any way harm her (whew!). However, as I was looking at the picture, if the ostrich did decide to attack my sister's hat and topple it to the ground, the situation would have illustrated a concept related to work.

Assuming that the ostrich applies a constant force, the work equation for the situation would be:

If my sister were as tall as the ostrich, the ostrich would have exerted less force on the hat because the force would have been along the direction of the displacement. However, as my sister is shorter than the ostrich, the force exerted by the ostrich is greater because it's at an angle theta versus a 0 degrees angle.