Question

ai mi is 1.45 meters tall. at 11 a.m., she measures the length of a trees shadow to be 27.65 meters. she stands 22.8 meters away from the tree, so that the tip of her shadow meets the tip of the trees shadow. find the height of the tree to the nearest hundredth of a meter.

Explanation:

Step1: Find the length of Ai Mi's shadow

The length of Ai Mi's shadow is \(27.65 - 22.8=4.85\) meters.

Step2: Set up a proportion

Let \(h\) be the height of the tree. We use the proportion \(\frac{\text{height of Ai Mi}}{\text{length of Ai Mi's shadow}}=\frac{\text{height of tree}}{\text{length of tree's shadow}}\).
So \(\frac{1.45}{4.85}=\frac{h}{27.65}\).

Step3: Solve for \(h\)

Cross - multiply: \(4.85h = 1.45\times27.65\).
First, calculate \(1.45\times27.65 = 1.45\times(27 + 0.65)=1.45\times27+1.45\times0.65 = 39.15+0.9425 = 40.0925\).
Then \(h=\frac{40.0925}{4.85}\).
\(h = 8.2664948\approx8.27\)

Answer:

\(8.27\) meters