George is 1.94 meters tall and wants to find the height of a tree in his yard. He started at the base of the tree and walked 10.20 meters along the shadow of the tree until his head was in a position where the tip of his shadow exactly overlaps the end fo the tree top's shadow. He is now 5.1 meters from the end of the shadows. How tall is the tree?

Question

Mathematics

Isabelle Benson

7 December, 09:29

George is 1.94 meters tall and wants to find the height of a tree in his yard. He started at the base of the tree and walked 10.20 meters along the shadow of the tree until his head was in a position where the tip of his shadow exactly overlaps the end fo the tree top's shadow. He is now 5.1 meters from the end of the shadows. How tall is the tree?

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Answers (1)

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Hope · Answer 1

Draw a diagram to illustrate problem as shown below.

Let h = the height of the tree.

Because ΔABC ~ ΔADE, therefore

DE/BC = AD/AB

That is,

h/1.94 = (5.1 + 10.2) / 5.1 = 3

h = 1.94*3 = 5.82 m

Answer: 5.82 m