Abuilding casts a shadow 48 feet long. at the same time, a 40 foot tall flagpole casts a shadow 9.6 feet long. what is the height of the building?

We solve this using proportion, so

shadow : height : : shadow : height

48 : x : : 9.6 : 40

48/x = 9.6/40

Taking reciprocal, we get

x/48 = 40/9.6

Multiply by 48 on both sides, we get

48 * x/48 = 48 * 40/9.6

x = 1920/9.6

x = 200 feet

Hence the height of the building is 200 feet.