Question

christian is 1.35 meters tall. at 10 a.m., he measures the length of a tree’s shadow to be 38.65 meters. he stands 34.4 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.

Explanation:

Step1: Find length of Christian's shadow

The length of Christian's shadow is $38.65 - 34.4=4.25$ meters.

Step2: Set up proportion

Since the triangles formed by Christian and his shadow, and the tree and its shadow are similar, the ratios of height to shadow - length are equal. Let the height of the tree be $h$. We have the proportion $\frac{h}{38.65}=\frac{1.35}{4.25}$.

Step3: Solve for $h$

Cross - multiply: $4.25h=1.35\times38.65$. Then $h = \frac{1.35\times38.65}{4.25}$. Calculate $1.35\times38.65 = 52.1775$, and $\frac{52.1775}{4.25}\approx12.28$ meters.

Answer:

$12.28$ meters