The height of the building is 210 feet.
Explanation
A 42 feet tall flagpole casts a shadow 9.2 feet long. That means, the ratio of the length of flagpole to the length of its shadow will be: [tex]\frac{42}{9.2}[/tex]
Now, a building casts a shadow 46 feet long. Suppose the height of the building is [tex]x[/tex] feet.
As the ratio will be same for Flagpole and Building at same time, so....
[tex]\frac{x}{46}=\frac{42}{9.2}\\ \\ 9.2x=46*42\\ \\ x=\frac{46*42}{9.2}=\frac{1932}{9.2}=210[/tex]
So, the height of the building is 210 feet.
