Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.

a painter needs to measure the height from the ground to the base of a 2nd story window. he props his ladder against the base of the window. he finds the height from one rung of the ladder to the point on the ground below it, and the distance from that point to the base of the ladder. this is shown in the figure.

image of a ladder propped against a window with points x, y, z, w, v. note: figure is not drawn to scale.

if xy = 8 inches, wy = 24 inches, and xz = 48 inches, the height from the ground to the base of the window is □ inches.

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Explanation:

Step1: Identify Similar Triangles

Triangles \( \triangle WXY \) and \( \triangle VXZ \) are similar (by AA similarity, as both are right triangles and share \( \angle X \)).

Step2: Set Up Proportion

For similar triangles, the ratios of corresponding sides are equal. So, \( \frac{WY}{VZ} = \frac{XY}{XZ} \).
Substitute the known values: \( \frac{24}{VZ} = \frac{8}{48} \).

Step3: Solve for \( VZ \)

Cross - multiply: \( 8\times VZ = 24\times48 \).
First, calculate \( 24\times48 = 1152 \).
Then, \( VZ=\frac{1152}{8}=144 \).

Answer:

144