Question

find v.
write your answer as a whole number or a decimal. do not round.
v = \boxed{} meters

Explanation:

Step1: Identify similar triangles

Triangles \( \triangle CGD\) and \( \triangle FED\) are similar. Because \( \angle CGD=\angle FED = 90^{\circ}\), and \( \angle CDG=\angle FDE\) (vertically - opposite angles).

Step2: Use the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal. That is \(\frac{CG}{FE}=\frac{GD}{DE}\).
We know that \(CG = 62\) m, \(FE=43.4\) m, \(GD = 45\) m, and \(DE = v\).
Substitute the values into the proportion: \(\frac{62}{43.4}=\frac{45}{v}\).
Cross - multiply: \(62v=43.4\times45\).
First, calculate \(43.4\times45=(40 + 3.4)\times45=40\times45+3.4\times45=1800+153 = 1953\).
Then, solve for \(v\): \(v=\frac{1953}{62}\).
\(v = 31.5\)

Answer:

\(v = 31.5\) meters