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
