Question

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

Explanation:

Step1: Prove similarity of triangles

Since \(\angle CAB=\angle EAD\) (vertically - opposite angles) and \(\angle B = \angle D=90^{\circ}\), by the AA (Angle - Angle) similarity criterion, \(\triangle ABC\sim\triangle ADE\).

Step2: Use the property of similar triangles

For similar triangles \(\triangle ABC\) and \(\triangle ADE\), the ratios of their corresponding sides are equal. That is \(\frac{AC}{AE}=\frac{BC}{DE}\).
We know that \(AC = 17\) m, \(AE=34\) m, and \(DE = 30\) m. Let \(BC = u\).
Substituting the values into the proportion \(\frac{17}{34}=\frac{u}{30}\).

Step3: Solve for \(u\)

Cross - multiply: \(34u=17\times30\).
Then \(u=\frac{17\times30}{34}\).
Simplify: \(u = 15\).

Answer:

\(15\)