A flagpole casts a showdown 15 feet long the 6 foot tall man casts a shadow 4 feet long how tall is the flag pole

Set it up as a ratio:

mans shadow over mans height (4/6) equals flag pole shadow over flag pole height (15/x)

set them to equal each other:

4/6 = 15/x

cross multiply: 4*x = 4x, 15*6 = 90

so you have 4x = 90

now divide both sides by 5 to solve for x, which is the height of the flag pole:

x = 90 / 4 = 22.5 feet tall