Question

question
kayla is 1.85 meters tall. at 12 noon, she measures the length of a tree’s shadow to be 28.15 meters. she stands 23.1 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.
(diagram is not to scale.)
answer attempt 2 out of 2

Explanation:

Step1: Find length of Kayla's shadow

The length of the tree's shadow is 28.15 meters and Kayla stands 23.1 meters away from the tree. So the length of Kayla's shadow is $28.15 - 23.1=5.05$ meters.

Step2: Set up proportion

Since the triangles formed by Kayla and her shadow, and the tree and its shadow are similar, the ratios of height to shadow - length are equal. Let $h$ be the height of the tree. We have the proportion $\frac{h}{28.15}=\frac{1.85}{5.05}$.

Step3: Solve for h

Cross - multiply to get $5.05h=1.85\times28.15$. Then $h = \frac{1.85\times28.15}{5.05}$. Calculate $1.85\times28.15 = 52.0775$ and $\frac{52.0775}{5.05}\approx10.31$ meters.

Answer:

10.31 meters