For a project in his Geometry class, Oliver uses a mirror on the ground to measure the height of his school building. He walks a distance of 8.65 meters from the building, then places a mirror on flat on the ground, marked with an X at the center. He then walks 2.7 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.65 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.