Question

A 24-foot flagpole casts a 46-foot shadow. The building next to it casts a 90-foot shadow. Find the height of the building to the nearest tenth.

A. 47.0 ft
B. 48.5 ft
C. 51.3 ft
D. 62.8 ft

Answer 1

The height of the building is found using similar triangles and proportion, which yields 47.0 feet as the height to the nearest tenth.

Step-by-step explanation:

Let's solve the problem about the height of a building by using the concept of similar triangles. The information given is that a 24-foot flagpole casts a 46-foot shadow, while the adjacent building casts a 90-foot shadow. We're assuming that the sun's rays are coming in at the same angle for both the flagpole and the building, which allows us to use proportions to find the height of the building.

First, we'll set up the proportion based on the similar triangles:

Flagpole height/Flagpole shadow = Building height/Building shadow

24 ft / 46 ft = Building height / 90 ft

Now, solve for the Building height:

(Building height) = (24 ft) * (90 ft) / 46 ft

Building height = 46.9565 ft, rounded to the nearest tenth gives 47.0 ft.

Therefore, the height of the building to the nearest tenth is 47.0 feet, which corresponds to option A.