For a project in her Geometry class, Chloe uses a mirror on the ground to measure the height of her school's football goalpost. She walks a distance of 13.65 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then walks 4.7 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.65 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.