Question

a 20-foot flagpole casts a 6-foot shadow. how tall is a nearby building that casts a 30-foot shadow (assume the sha at the same time of the day and both the flagpole and the building face the sun at approximately the same angle)?

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the building. The ratio of height to shadow length should be equal for the flagpole and the building. So, \(\frac{20}{6}=\frac{h}{30}\).

Step2: Solve for \( h \)

Cross - multiply: \(6h = 20\times30\).
Calculate \(20\times30 = 600\), so \(6h=600\).
Divide both sides by 6: \(h=\frac{600}{6}=100\).

Answer:

The height of the building is 100 feet.