Question

a lamppost is 6 feet high and casts an 8 foot shadow. at the same time of day, a flagpole near the lamppost casts a 20 foot shadow. using the pro
a. $\frac{12}{5}$ ft
b. 15 ft
c. 18 ft
d. $\frac{80}{3}$ ft

Explanation:

Step1: Set up proportion

Since the ratios of height to shadow - length are equal for similar - triangles formed by the lamp - post and the flag - pole, we can set up the proportion $\frac{h_1}{s_1}=\frac{h_2}{s_2}$, where $h_1$ is the height of the lamp - post, $s_1$ is the shadow length of the lamp - post, $h_2$ is the height of the flag - pole, and $s_2$ is the shadow length of the flag - pole. Here, $h_1 = 6$ ft, $s_1=8$ ft, and $s_2 = 20$ ft. So the proportion is $\frac{6}{8}=\frac{H}{20}$.

Step2: Solve for $H$

Cross - multiply the proportion: $8H=6\times20$. Then $8H = 120$. Divide both sides by 8: $H=\frac{120}{8}=15$ ft.

Answer:

B. 15 ft