Question

A flagpole casts a shadow that is 16 feet long. At the same time, a person standing nearby who is 5 feet 6 inches tall casts a

shadow that is 44 inches long. How tall is the flagpole?

Answer 1

32ft

Explanation:

Let's convert both the height of the person and the length of their shadow to feet so we can make a comparison.

1 foot = 12 inches

So the person's height in feet is:

5 feet + 6 inches / 12 inches/foot = 5.5 feet

The rule applied here is the concept of similar triangles. If the shadow of the person and the shadow of the flagpole are in the same proportion to their respective heights, then the two triangles formed by their heights and shadows are similar triangles. This means that the ratio of their heights to their shadow lengths is constant.

So, we can set the ratio of the person's height to their shadow length equal to the ratio of the flagpole's height to its shadow length and solve for the flagpole's height. This is done using the formula:

(person's height) / (person's shadow length) = (flagpole's height) / (flagpole's shadow length)

This is known as the proportionality rule, which states that two similar figures have the same ratios of corresponding sides.

Now, we have:

5.5/44 inches = x/16 feet

Cross multiplying, we get:

5.5 * 16 = x * 44

Solving for x:

x = 5.5 * 16 / 44

x = 32 feet

Therefore, the height of the flagpole is 32 feet.