Question

2
a building inspector is attempting to determine the height of a newly-constructed building using the buildings shadow. in the late
afternoon, the shadow of the building is 80 ft long. at the same time, a mailbox that is 4 ft tall has a shadow that is 3.2 ft long.
what is the height of the building?

a. 100 ft

b. 64 ft

c. 256 ft

d. 80.8 ft

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the building. The ratio of height to shadow length should be equal for the building and the mailbox. So, \(\frac{h}{80}=\frac{4}{3.2}\).

Step2: Solve for \( h \)

Cross - multiply: \( 3.2h = 4\times80 \). Calculate \( 4\times80 = 320 \). Then, \( h=\frac{320}{3.2}=100 \).

Answer:

A. 100 ft