Question

the sun casts a shadow on a building and a flagpole. the building is 100 feet tall and its shadow is 25 feet. the flagpole has a shadow of 5 feet. two triangles shown are similar.
*diagram not drawn to scale.
how tall is the flagpole?
a. 10 feet
b. 20 feet
c. 40 feet
d. 80 feet

Explanation:

Step1: Set up proportion for similar triangles

Let \( h \) be the height of the flagpole. Since the triangles are similar, the ratios of corresponding sides are equal. So, \(\frac{\text{Height of building}}{\text{Shadow of building}}=\frac{\text{Height of flagpole}}{\text{Shadow of flagpole}}\), which gives \(\frac{100}{25}=\frac{h}{5}\).

Step2: Solve for \( h \)

Cross - multiply: \( 25h = 100\times5 \). Then \( 25h=500 \). Divide both sides by 25: \( h=\frac{500}{25}=20 \).

Answer:

B. 20 feet