Question

travis is 1.85 meters tall. at 2 p.m., he measures the length of a tree’s shadow to be 39.55 meters. he stands 35.4 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. (diagram is not to scale.)

Explanation:

Step1: Find length of Travis's shadow

The length of the tree's shadow is 39.55 meters and Travis stands 35.4 meters away from the tree. So the length of Travis's shadow is $39.55 - 35.4=4.15$ meters.

Step2: Set up proportion

Since the triangles formed by Travis and his 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 $\frac{h}{39.55}=\frac{1.85}{4.15}$.

Step3: Solve for $h$

Cross - multiply the proportion: $4.15h=1.85\times39.55$. Then $h = \frac{1.85\times39.55}{4.15}$. Calculate $1.85\times39.55 = 73.1675$. Then $h=\frac{73.1675}{4.15}\approx17.63$ meters.

Answer:

$17.63$ meters