Question

a pole that is 3.2 m tall casts a shadow that is 1.09 m long. at the same time, a nearby tower casts a shadow that is 39.5 m long. how tall is the tower? round your answer to the nearest meter.

Explanation:

Step1: Set up the proportion

Let \( h \) be the height of the tower. Since the ratio of height to shadow length is the same for both the pole and the tower, we have the proportion \(\frac{\text{height of pole}}{\text{shadow length of pole}}=\frac{\text{height of tower}}{\text{shadow length of tower}}\), i.e., \(\frac{3.2}{1.09}=\frac{h}{39.5}\).

Step2: Solve for \( h \)

Cross - multiply: \(1.09h = 3.2\times39.5\). First, calculate \(3.2\times39.5=126.4\). Then \(h=\frac{126.4}{1.09}\approx116\).

Answer:

\(116\)