Question

Madelyn is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 39.75 meters. She stands 34.9 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.

Answer 1

The relationship between her height and the tree's is an illustration of ratios and proportions

The height of the tree is approximately 2.11 meters

Her height is represented as:

$\mathbf{h =1.85}$

At 12 noon, the length of the tree's shadow and her distance from the shadow are given as:

$\mathbf{D =39.75}$

$\mathbf{d =34.9}$

To calculate the height (H) of the tree, we make use of the following equivalent ratios

$\mathbf{H : h =D : d}$

So, we have:

$\mathbf{H : 1.85 =39.75 : 34.9}$

Express ratio as fraction

$\mathbf{\frac{H }{ 1.85 }=\frac{39.75 }{ 34.9}}$

Multiply both sides by 1.85

$\mathbf{H=1.85 \times \frac{39.75 }{ 34.9}}$

$\mathbf{H=2.11}$

Hence, the height of the tree is approximately 2.11 meters

Read more about ratios and proportions at:

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