Question

#3
a 12 - foot flagpole casts a shadow that is 5 feet long.
at the same time, a nearby telephone pole casts a shadow that is 12.5 feet long.
what is the height of the telephone pole, x?
5.2 feet 15 feet
18.5 feet 30 feet
show work: \all equivalent ratios\
slope=
5.2 ft.
15 ft.
18.5 ft.
30 ft.

Explanation:

Step1: Set up the proportion

Since the triangles are similar (due to same - time sunlight), the ratios of height to shadow length are equal. Let the height of the flagpole be \(h_1 = 12\) ft, shadow of flagpole \(s_1=5\) ft, height of telephone pole be \(h_2=x\) ft, and shadow of telephone pole \(s_2 = 12.5\) ft. The proportion is \(\frac{h_1}{s_1}=\frac{h_2}{s_2}\).

Step2: Substitute the values into the proportion

Substitute \(h_1 = 12\), \(s_1 = 5\), and \(s_2=12.5\) into \(\frac{h_1}{s_1}=\frac{h_2}{s_2}\), we get \(\frac{12}{5}=\frac{x}{12.5}\).

Step3: Solve for \(x\)

Cross - multiply: \(5x=12\times12.5\). Then \(5x = 150\). Divide both sides by 5: \(x=\frac{150}{5}=30\).

Answer:

d. 30 ft