Question

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

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle GCF\sim\triangle GDE\) (by AA similarity, as \(\angle GCF=\angle GDE = 90^{\circ}\) and \(\angle G\) is common), the ratios of corresponding sides are equal. That is \(\frac{FC}{ED}=\frac{GC}{GD}\).
We know \(FC = 27.3\) m, \(GC=56\) m, \(GD=56 + 24=80\) m, and \(ED = y\).
Substituting the values into the proportion \(\frac{27.3}{y}=\frac{56}{80}\).

Step2: Solve the proportion for \(y\)

Cross - multiply: \(56y=27.3\times80\).
First, calculate \(27.3\times80 = 2184\).
Then, \(y=\frac{2184}{56}\).
Divide \(2184\) by \(56\): \(y = 39\).

Answer:

\(39\)