Question

find z.
write your answer as a whole number or a decimal. do not round.
z = yards

Explanation:

Step1: Determine similar triangles

Triangles \( \triangle BCF\) and \( \triangle DEF\) are similar. Because \(\angle BCF=\angle DEF = 90^{\circ}\) and \(\angle BFC=\angle DFE\) (vertically - opposite angles).

Step2: Set up the proportion

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{BC}{DE}=\frac{CF}{EF}\). Let \(BC = z\), \(DE = 13.2\) yd, \(CF = 44.8\) yd, and \(EF=22.4\) yd.
Substituting the values into the proportion: \(\frac{z}{13.2}=\frac{44.8}{22.4}\).

Step3: Solve for \(z\)

Cross - multiply: \(22.4z=13.2\times44.8\).
First, calculate \(13.2\times44.8 = 13.2\times(40 + 4.8)=13.2\times40+13.2\times4.8=528+63.36 = 591.36\).
Then, \(z=\frac{591.36}{22.4}\).
\(z = 26.4\).

Answer:

\(26.4\)