Question

jai is 1.45 meters tall. at 11 a.m., he measures the length of a tree’s shadow to be 39.55 meters. he stands 34.1 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.) answer attempt 1 out of 2

Explanation:

Step1: Find length of Jai's shadow

The length of Jai's shadow is $39.55 - 34.1=5.45$ meters.

Step2: Set up proportion

Since the triangles formed by Jai 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. Then $\frac{h}{39.55}=\frac{1.45}{5.45}$.

Step3: Solve for h

Cross - multiply to get $5.45h = 1.45\times39.55$. Then $h=\frac{1.45\times39.55}{5.45}$.
$1.45\times39.55 = 1.45\times(40 - 0.45)=1.45\times40-1.45\times0.45 = 58 - 0.6525 = 57.3475$.
$h=\frac{57.3475}{5.45}\approx10.52$ meters.

Answer:

$10.52$ meters