Question

find q.
write your answer as a whole number or a decimal. do not round.
q = meters

Explanation:

Step1: Use the property of similar triangles

Since \( \triangle FGE\sim\triangle FCD\) (by AA similarity, as \(\angle F\) is common and \(\angle FGE=\angle FCD = 90^{\circ}\)), the ratios of their corresponding sides are equal. That is \(\frac{FG}{FC}=\frac{q}{DC}\).

Step2: Substitute the given values

We know that \(FG = 9\) m, \(FC=9 + 9=18\) m, and \(DC = 11.2\) m. Substituting into \(\frac{FG}{FC}=\frac{q}{DC}\), we get \(\frac{9}{18}=\frac{q}{11.2}\).

Step3: Solve for \(q\)

Cross - multiply: \(18q=9\times11.2\). Then \(q=\frac{9\times11.2}{18}\). Simplify \(\frac{9\times11.2}{18}=\frac{11.2}{2}\).

Answer:

\(q = 5.6\) meters