Question

to estimate the height of a tree, adele waited until the tops of the shadows of the tree and the sign coincided. the sign is 2 meters tall and the signs shadow is 6.4 meters tall. the trees shadow is 9.4 meters long. determine the height of the tree to the nearest tenth of a meter. the tree is \boxed{} meters tall.

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the tree. Since the triangles are similar, the ratios of height to shadow length are equal. So we have \(\frac{h}{9.4}=\frac{2}{6.4}\).

Step2: Solve for \( h \)

Cross - multiply: \( h=\frac{2\times9.4}{6.4} \).
First, calculate the numerator: \( 2\times9.4 = 18.8 \).
Then, divide by the denominator: \( h=\frac{18.8}{6.4}=2.9375 \approx 2.9 \) (rounded to the nearest tenth).

Answer:

\( 2.9 \)