find the lamppost at the park

Question

To find the height of a lamppost at a park, Rachel placed a mirror on the ground 20 feet from the base of the lamppost. She then stepped back 4 feet so that she could see the top of the lamp post in the center of the mirror. Rachel's eyes are 5 feet 6 inches above the ground. What is the height, in feet, of the lamppost?

Answer 1

mirror on the ground 20 feet from base of the lamp post, she's 5 1/2 feet tall

she steps back 4 feet to look at the top of the lamp post in the center of the mirror

how tall is the lamp post??

construct a right triangle, with height = height of the lamp post

base = 20-4 = 16 feet

2nd right triangle has height = 5 1/2 feet and base = 4 feet

ratio of height to base is equal for both right triangles

x/20 = 5.5/4

x = 20(5.5)/4 = 5(5.5)

= 27.5 feet = height of the lamp post