A 8-foot tall man is standing beside a 32-foot flagpole. The flagpole is

casting a shadow of 22.5 feet. How much longer is the shadow cast by the

flagpole than the shadow cast by the man?

The flagpole's shadow is 16.875 feet longer than the man's shadow

Step-by-step explanation:

The total length of the shadow is expressed by taking its actual length by a factor that depends on the position of the sun which is constant for the man too. The expression is as follows;

Height of the shadow=actual height of the flagpole*factor

where;

length of the flagpole's shadow=22.5 feet

actual height of the flagpole=32 feet

factor=f

replacing;

22.5=32*f

32 f=22.5

f=22.5/32

f=0.703125

Using this factor in the expression below;

Length of man's shadow=actual height of man*factor

where;

length of man's shadow=m

actual height of man=8 feet

factor=0.703125

replacing;

length of man's shadow=8*0.703125=5.625 feet

Determine how much longer the flagpole's shadow is as follows;

flagpoles shadow-man's shadow=22.5-5.625=16.875 feet

The flagpole's shadow is 16.875 feet longer than the man's shadow