Question

A person stands 10 meters from a lamppost at night. If the person is 2 meters tall and the lamppost is 6 meters tall, how long is their shadow cast by the lamp?

Answer 1

5 meters

Explanation:

The height of the lamppost above the person is twice the height of the person, so the distance between the lamppost and person is twice the length of the person's shadow. (A diagram can help you see this.)

The person's shadow is (10 m)/2 = 5 m long.

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Check

The tip of the shadow is 15 m from the lamppost, 2.5 times the height of the lamp. The tip of the shadow is also 5 m from the person, 2.5 times the height of the person. The triangles involved are similar.