The sun shines down on a flagpole and on a mailbox at the same time casting shadows and making similar triangles. The mailbox is 4 ft tall and casts a shadow 3 ft long. The flagpole's shadow is 12 ft long. How tall is the flagpole?
To find the height of the flagpole, we can set up a proportion using the similar triangles formed by the flagpole and its shadow and the mailbox and its shadow.
Let x represent the height of the flagpole.
Using the proportion:
4/3 = x/12
Cross multiplying gives:
3x = 48
Dividing by 3 on both sides:
x = 16
Therefore, the flagpole is 16 ft tall.