Abuilding casts a shadow 47 feet long. at the same time, a 42‐foot‐tall flagpole casts a shadow 9.4 feet long. what is the height of the building? show work.

210 feet

To answer this question you need to know the ratio of shadow with the actual object. In this case, 42 feet flagpole cast 9.4 feet shadow. Then the ratio is:
42feet/9.4 feet= 4.468

That means the actual height is 4.468 times of shadow length. After that, you can multiply the ratio with the shadow to know the object actual size. It would be: 47 feet x 4.468=  210 feet.