Question

1. in the figure, △fgi is similar to △jhi. what is the height h of the flagpole when it is 256.5 feet from the statue?

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle FGI\sim\triangle JHI\), the ratios of their corresponding sides are equal. That is \(\frac{h}{305}=\frac{274.5 - 256.5}{274.5}\)

Step2: Simplify the right - hand side of the equation

First, calculate \(274.5−256.5 = 18\). So the equation becomes \(\frac{h}{305}=\frac{18}{274.5}\)

Step3: Solve for \(h\)

Cross - multiply: \(274.5h=18\times305\)

\(274.5h = 5490\)

Then \(h=\frac{5490}{274.5}\)

\(h = 20\)

Answer:

\(20\)