Irene places a mirror on the ground 24ft away from the base of an oak tree. she walks backward until she can see the top of the tree in the middle of the mirror. at that point, irene's eyes are 4 ft from the mirror. at that point, irene's eyes are 5.5ft above the ground, and her feet are 4 ft from the mirror. how tall is the oak tree? explain.

First, illustrate the problem:

24 feet is the distance between the tree and the mirror. 
4 feet is the distance from Irene's eyes to the mirror. 
5.5 feet is the distance of Irene's eyes from the ground.
4 feet is the distance of Irene from the mirror

From this, we can draw a right triangle and then use the Pythagorean theorem to solve for the height of the oak tree. Also, we have an option to use ratio and proportion between two similar triangles.