To find the height of the flagpole, we can set up a proportion using the given information.
Let's define the variables:
h1 = height of the man (1.8 m)
s1 = shadow length of the man (4.32 m)
s2 = shadow length of the flagpole (12.8 m)
h2 = height of the flagpole (unknown)
Since the shadow is directly proportional to the height, we can write the proportion:
s1/h1 = s2/h2
Substituting the given values into the proportion:
4.32/1.8 = 12.8/h2
To find the height of the flagpole (h2), we can solve this proportion.
Cross multiply the equation:
(4.32)(h2) = (1.8)(12.8)
Now solve for h2:
h2 = (1.8)(12.8) / 4.32
Calculating the value:
h2 = 6.4 m
Therefore, the height of the flagpole is 6.4 meters.