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| Math Central | Quandaries & Queries |
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Question from maaz, a student: Hello 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,
Penny
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