Question

nicole is 1.55 meters tall. at 2 p.m., she measures the length of a tree’s shadow to be 30.05 meters. she stands 25.6 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 1 out of 2

Explanation:

Step1: Find the length of Nicole's shadow

The length of Nicole's shadow is \(30.05 - 25.6=4.45\) meters.

Step2: Set up the proportion

Since the triangles (formed by Nicole and her shadow, and the tree and its shadow) are similar, we can set up the proportion \(\frac{\text{Nicole's height}}{\text{Nicole's shadow length}}=\frac{\text{Tree's height}}{\text{Tree's shadow length}}\). Let \(h\) be the height of the tree. Then \(\frac{1.55}{4.45}=\frac{h}{30.05}\).

Step3: Solve for \(h\)

Cross - multiply: \(4.45h = 1.55\times30.05\). First, calculate \(1.55\times30.05 = 1.55\times(30 + 0.05)=1.55\times30+1.55\times0.05 = 46.5+0.0775 = 46.5775\). Then \(h=\frac{46.5775}{4.45}\). \(h=\frac{46.5775}{4.45}=10.467\approx10.47\)

Answer:

\(10.47\)