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# tree

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One way to find the height of a tall tree is to measure its shadow and compare that with the shadow and compare that with the shadow of an object whose height is unknown. Use this idea to write and solve a proportion based on this picture, to calculate the height of the tree.

waffles  May 22, 2017

#1
+1493
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The height of the tree is $$24m$$

In this picture, we are using 1m and 0.75m as our reference. Here's our proportion that the question asks for.
Let h = height of tree:

$$\frac{1}{0.75}=\frac{h}{18}$$ Cross multiply and solve for h

$$18*1=0.75h$$ I prefer fractions to decimals, so I will convert 0.75 to 3/4.

$$18=\frac{3}{4}h$$ To get rid of the fraction, multiply both sides by 4/3.

$$\frac{4}{3}*18=\frac{3}{4}h*\frac{4}{3}$$ Simplify both sides of the equation

$$h=\frac{18*4}{3}$$

$$h=\frac{72}{3}=24m$$ Of course, include units in your final answer!

TheXSquaredFactor  May 22, 2017
Sort:

#1
+1493
+1

The height of the tree is $$24m$$

In this picture, we are using 1m and 0.75m as our reference. Here's our proportion that the question asks for.
Let h = height of tree:

$$\frac{1}{0.75}=\frac{h}{18}$$ Cross multiply and solve for h

$$18*1=0.75h$$ I prefer fractions to decimals, so I will convert 0.75 to 3/4.

$$18=\frac{3}{4}h$$ To get rid of the fraction, multiply both sides by 4/3.

$$\frac{4}{3}*18=\frac{3}{4}h*\frac{4}{3}$$ Simplify both sides of the equation

$$h=\frac{18*4}{3}$$

$$h=\frac{72}{3}=24m$$ Of course, include units in your final answer!

TheXSquaredFactor  May 22, 2017

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