Question

1. what is xy?

Explanation:

Step1: Identify similar triangles

The two right - angled triangles $\triangle UVW$ and $\triangle XYZ$ are similar because they have two equal angles: $23^{\circ}$ and $90^{\circ}$.

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. We can set up the proportion $\frac{XY}{UV}=\frac{YZ}{VW}$.
We know that $UV = 10$ ft, $VW=24$ ft, and $YZ = 10$ ft. Let $XY = x$. Then $\frac{x}{10}=\frac{10}{24}$.

Step3: Solve for $XY$

Cross - multiply to get $24x=10\times10 = 100$. Then $x=\frac{100}{24}=\frac{25}{6}\approx4.17$ ft.

Answer:

$\frac{25}{6}$ ft