Math CentralQuandaries & Queries


Question from maaz, a student:

I am having trouble with this question:

Lizzie, who is 6 feet tall, stands in her driveway at night, exactly 24 feet from the base of a spotlight, and casts a shadow that is 12 feet long if her friend Hannah who is 5 feet tall decides to stand next to lizzie how long will her shadow be?

Hi Maaz,

I can help you get started. In the diagram below A is the base of the spotlight pole, E is the top of the spotlight pole, B is Lizzie's feet, D is Lizzie's head and C is the tip of Lizzie's shadow.


|AB| is 24 feet, |BC| is 12 feet and |BD| is 6 feet. Let the height of the spotlight pole be h feet.

Triangles EAC and DBC are similar. use this fact to find h, the height of the pole.

Draw a similar diagram for Hannah. Let s be the length of Hannah's shadow. Use similar triangles to find s.

Write back if you need more assistance,


About Math Central


Math Central is supported by the University of Regina and the Imperial Oil Foundation.
Quandaries & Queries page Home page University of Regina