A triangle is formed by the building's height and shadow. Another triangle is formed by the flagpole's height and shadow. Using the following diagram, find the height of the building.
BUILDING SHADOW = 24FT
FLAGPOLE = 40FT
To find the height of the building, we can set up a proportion with the two triangles formed by the building and the flagpole.
Let \( x \) be the height of the building.
Using similar triangles, we have:
\[
\frac{\text{height of building}}{\text{building shadow}} = \frac{\text{height of flagpole}}{\text{flagpole shadow}}
\]
\[
\frac{x}{24} = \frac{40}{16}
\]
\[
\frac{x}{24} = \frac{5}{2}
\]
Cross multiply:
\[ 2x = 24 \times 5 \]
\[ 2x = 120 \]
\[ x = \frac{120}{2} \]
\[ x = 60 \]
Therefore, the height of the building is 60 feet.