Question

Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot. Find the geometric mean of the pair of numbers. A. 20 ft B. 38.4 ft C. 55 ft D. 25 ft

Answer 1

Refer to the diagram below for the sketch of the position of the mirror, Michelle, and the flagpole.

Using similar triangle concept, to find the height of the flagpole, we first need to find out the scale factor of the horizontal distance. 
We write this as ratio
Mirror to Michelle : Mirror to Flagpole
            12ft             :             48ft
             1                :               4

So the ratio of the height is
Michelle : Flagpole
     1         :       4
    5ft       :      20ft

Answer: A