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\Grace is 1.65 meters tall. At 3 p.m., she measures the length of a tree's shadow to be 25.35 meters. She stands 20.9 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Sagot :

MrRoyal

Grace's height and the tree's height are related by equivalent ratios

The height of the tree is 2.00 meters

Grace's height is given as:

[tex]\mathbf{h = 1.65}[/tex]

When she measured the length of the tree's shadow, we have:

[tex]\mathbf{l = 20.9m}[/tex] --- the length of her shadow

[tex]\mathbf{L = 25.35m}[/tex] --- the length of the tree's shadow

The height (H) of the tree is calculated using the following equivalent ratio

[tex]\mathbf{h:H = l:L}[/tex]

Substitute known values

[tex]\mathbf{1.65:H = 20.9:25.35}[/tex]

Express as fractions

[tex]\mathbf{\frac H{1.65} =\frac{25.35}{20.9}}[/tex]

Multiply both sides by 1.65

[tex]\mathbf{H=\frac{25.35}{20.9} \times 1.65}[/tex]

Simplify

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

Hence, the approximated height of the tree is 2.00 meters

Read more about equivalent ratios at:

https://brainly.com/question/13513438

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