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Aaden is 1.75 meters tall. At 11 a.m., he measures the length of a tree's shadow to be 37.65 meters. He stands 32.9 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Sagot :

MrRoyal

The relationship between Aaden and the tree's height is an illustration of equivalent ratio

The height of the tree is 2.00 meters

At 11 a.m, we have:

[tex]\mathbf{Aaden = 1.75m}[/tex]

[tex]\mathbf{Tree\ Shadow = 37.65m}[/tex]

[tex]\mathbf{Aaden\ Shadow = 32.9m}[/tex]

So, we make use of the following equivalent ratio

[tex]\mathbf{Aaden : Tree = Aaden\ Shadow : Tree\ Shadow}[/tex]

This gives

[tex]\mathbf{1.75: Tree = 32.9: 37.65}[/tex]

Express as fractions

[tex]\mathbf{\frac{Tree}{1.75} = \frac{37.65}{32.9}}[/tex]

Multiply both sides by 1.75

[tex]\mathbf{Tree = \frac{37.65}{32.9} \times 1.75}[/tex]

[tex]\mathbf{Tree = 2.00}[/tex]

Hence, the height of the tree is 2.00 meters

Read more about equivalent ratios at:

https://brainly.com/question/18441891

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