Question

1. julia stands 28 feet from a flagpole and casts a 7 - foot shadow. if julia is 5 feet tall then how tall is the flagpole?

Explanation:

Step1: Determine the total base length for the flagpole's triangle

The distance from Julia to the flagpole is 28 feet, and her shadow is 7 feet. So the base length for the flagpole's similar triangle is \(28 + 7=35\) feet.

Step2: Set up the proportion for similar triangles

Let \(h\) be the height of the flagpole. Since the triangles are similar, the ratios of height to base are equal. So \(\frac{5}{7}=\frac{h}{35}\)

Step3: Solve for \(h\)

Cross - multiply: \(7h = 5\times35\)
\(7h=175\)
Divide both sides by 7: \(h=\frac{175}{7} = 25\)

Answer:

The flagpole is 25 feet tall.