G.3.16.3 Indirect Measurement (Mirrors)

The angle of incidence of an object reflecting off a mirror is equal to the angle of reflection, so mirrors also make great contexts for using similar triangles! You can find the height of a very tall object by placing mirror on the ground so that when you stand back and look into the mirror you see the top edge of the object reflected in the mirror. When you do this, you have made 2 similar triangles! You'll need 3 measurements to get the height of the building:

  • your height
  • your distance to the mirror
  • the building's distance to the mirror
If the woman is 5.5 feet tall, she is 7 feet from the mirror and the building is 54 feet from the mirror, how tall is the building?