Question

a pole that is 2.8 m tall casts a shadow that is 1.02 m long. at the same time, a nearby building casts a shadow that is 48.5 m long. how tall is the building? round your answer to the nearest meter.

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the building. Using the proportion \(\frac{\text{height of pole}}{\text{shadow of pole}}=\frac{\text{height of building}}{\text{shadow of building}}\), so \(\frac{2.8}{1.02}=\frac{h}{48.5}\).

Step2: Solve for \( h \)

Cross - multiply: \( 1.02h = 2.8\times48.5 \). Then \( h=\frac{2.8\times48.5}{1.02} \). Calculate \( 2.8\times48.5 = 135.8 \), so \( h=\frac{135.8}{1.02}\approx133.14 \).

Answer:

\( 133 \)