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Henri's neighbor wants to cut down a tree, but Henri is worried because it will fall on his garage which is 42 feet from the tree. The neighbor decided to measure using the shadow it was 47.2 feet. Henri put his yardstick ( 1 yard = 3 feet) next to the tree, and the yardsticks cast a shadow of 3.5 feetHow tall is the tree? (show how got the answerwill the tree hit henri's garage if it falls the wrong way? EXPLAIN YOUR ANSWER

User Chris Zheng
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1 Answer

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29 votes

We are given that a tree casts a shadow of 47.2 feet and we are asked to determine its height. We are also given that a yardstick cast a shadow of 3.5 feet. The yardstick and the tree form right triangles as shown in the next diagram:

Since both the tree and the yardstick have the same angle of incidence of light this means that both triangles are similar triangles, and therefore, we have the following relationship:


(T)/(47.2)=(3)/(3.5)

This is, the ratio between the opposite side and the adjacent sides of both triangles is the same. Now we solve for T by multiplying both sides by 47.2:


47.2*(T)/(47.2)=(3)/(3.5)*47.2

Solving the operations:


T=40.46feet

Therefore, the height of the tree is 40.46 feet.

For the second part we have:

If the tree falls then the length of 40.46 feet wouldn't be enough to hit the garage.

Henri's neighbor wants to cut down a tree, but Henri is worried because it will fall-example-1
Henri's neighbor wants to cut down a tree, but Henri is worried because it will fall-example-2
User Aditya Santoso
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