Aboy that is 6 feet tall casts a shadow that is 3.5 feet long. if a pole cast a shadow 12.2 feet long, then how tall is the pole?

This is a problem of "similar triangles", which means that the ratio of side lengths is the same for both triangles.  In this case we are talking about the "height" and "base" sides so:

ph/ps=bh/bs

The pole height/pole shadow is equal to the boy height/boy shadow

h/12.2=6/3.5  multiply both sides by 12.2

h=73.2/3.5

h=732/35 ft

h≈20.91 ft (to nearest hundredth of a foot)