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Please help me with this geometry problem!!!

Please help me with this geometry problem!!!-example-1
User Ben Manes
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1 Answer

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There are infinitely many ways to answer this, but one way could be this.

There is a 30 foot tree that casts a 25 foot shadow. A sign post nearby casts a 15 foot shadow. How tall is the sign post? Both the tree and the sign post are standing completely vertical. The ground is completely flat and horizontal.

Note: Since the sun is very far away, the light rays are effectively parallel which allows for the two bottom acute angles to be nearly the same value.

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If you're curious on how to solve such a question, then we can make a proportion like shown below. Cross multiply to isolate for x

30/25 = x/15

30*15 = 25*x

450 = 25x

25x = 450

x = 450/25

x = 18

The sign post is therefore 18 feet tall.

An alternative equation is 30/x = 25/15, which leads to the same solution.

User Kira Hao
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