Question

El Generico public high school got a new flagpole. But they completely forgot to buy a cord and NO ONE knows how tall the flagpole is! To find out, they decided to use similar figures! As the sun was setting, Bob the janitor set up a 5-foot stick next to the flagpole and compared shadows. The 5-foot stick cast an 8-foot shadow. The shadow of the flagpole was 32-feet long.

Answer 1

In measurement problems such as these, we can use proportional relationships to determine the length or measure of triangular sides.This works because the two figures are similar. Our proportion is going to have a variable since we do not know the height of one of the flagpoles. It will be set up as such: 

$\frac{5}{8}$ = $\frac{x}{32}$

We cross multiply, then divide to solve this proportion.

32 x 5 = 160. 

160/8 = 20. 

This means the height of the flagpole is 20 feet high. To fit the height of the flag pole, the cord the school should buy for the flagpole should be 20 feet long.