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Finding the length of a shadow

by Morgan
(Washington )












































I'm 6 ft tall and I cast a 12 ft shadow.

I want to find out the length a 5 ft tree's shadow.

How would I do that?

Comments for Finding the length of a shadow

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Jun 24, 2014
length a 5 ft tree's shadow
by: Staff


Answer

Part I


similar triangles:  calculating the length of a shadow 

*** Click to enlarge image ***




The two triangles shown are similar triangles.

Numerically, the ratio computed by dividing the length of any side of tree triangle by the length of the corresponding side of the human (similar) triangle will be the same value.

Therefore, when the length of the tree shadow is divided by the length of the human shadow, that ratio will be the exactly same as the tree height divided by the human height.

Mathematically, this can be expressed in the following equation:



(length of tree shadow) / (length of human shadow) = (tree’s height) / (human’s height)

Substitute the known values in the equation

length of the tree’s shadow = L (unknown)

length of human shadow = 12 feet

tree’s height = 5 feet

your height = 6 feet


(L) / (12) = (5) / (6)




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Jun 24, 2014
length a 5 ft tree's shadow
by: Staff


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Part II


using a proportion to calculate the length of a shadow 

*** Click to enlarge image ***





Solve for L

Multiply each side of the equation by 12

[(L) / (12)] * 12 = [(5) / (6)] * 12

Simplify the equation

(L / 12) * (12 / 1) = (5 / 6) * (12 / 1)

(L * 12) / (12 * 1) = (5 * 12) / (6 * 1)

(L * 12) / 12 = (5 * 12) / 6

The final solution

L * (12 / 12) = 5 * (12 / 6)

L * (1) = 5 * (2)

L = 10


1 - solve for the length of the shadow cast by the tree 

*** Click to enlarge image ***







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Jun 24, 2014
length a 5 ft tree's shadow
by: Staff


--------------------------------------------------




Part III


2 - solve for the length of the shadow cast by the tree 

*** Click to enlarge image ***





Final answer

Length of the tree’s shadow = 10 feet


length of the tree’s shadow – final answer 

*** Click to enlarge image ***







Thanks for writing.

Staff
www.solving-math-problems.com


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