Question

a pole that is 3.5 m tall casts a shadow that is 1.44 m long. at the same time, a nearby building casts a shadow that is 45.75 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. The ratio of height to shadow length is constant. So, \(\frac{3.5}{1.44}=\frac{h}{45.75}\)

Step2: Solve for \( h \)

Cross - multiply: \( h=\frac{3.5\times45.75}{1.44}\)
Calculate numerator: \( 3.5\times45.75 = 160.125\)
Then divide by 1.44: \( h=\frac{160.125}{1.44}\approx111.1979\)

Step3: Round to nearest meter

Rounding \( 111.1979\) to the nearest meter gives 111.

Answer:

111