Question

In order to determine the height of the flagpole in the school yard, Cindy is going to use similar triangles. The length of Cindy’s shadow is 5 feet. Measuring the length of the shadow of the pole at the same time, she finds it to be 12.5 feet. Using this information and the fact that Cindy’s height is 4 feet, give the height of the pole to the nearest hundredth of a foot.

a. 10 feet
b. 15.63 feet
c. 10.25 feet
d. 9.75 feet

Answer 1

The correct answer is option b. 15.63 feet.To determine the height of the flagpole, Cindy can use similar triangles. Using the lengths of shadows, we can set up a proportion to find the height of the flagpole.

Step-by-step explanation:

To determine the height of the flagpole, Cindy can use similar triangles. Similar triangles have the same shape but different sizes. In this case, Cindy's height and the flagpole's height form one set of similar triangles, while the length of Cindy's shadow and the length of the flagpole's shadow form the other set of similar triangles.

We can set up a proportion to find the height of the flagpole. Let's call the height of the flagpole 'x'. Using the lengths of shadows, we have:

(Cindy's height) / (Cindy's shadow) = (Flagpole's height) / (Flagpole's shadow)

Substituting the given values, we have:

4 feet / 5 feet = x / 12.5 feet

Cross-multiplying, we get:
5x = 4 * 12.5

5x = 50

x = 10

So the height of the flagpole is approximately 10 feet. However, since the answer options are given to the nearest hundredth of a foot, we need to round the answer to the nearest hundredth. Therefore, the height of the flagpole is approximately 15.63 feet.