Final answer:
Using the properties of similar triangles, the height of the flagpole can be calculated. Rachel's height to shadow ratio is equivalent to the flagpole's height to shadow ratio. The flagpole is 22.5 feet tall.
Step-by-step explanation:
To determine the height of the flagpole, we can use the property that similar triangles share the same shape and angles but are of different sizes. Here, we're comparing the triangle made by the flagpole and its shadow to the triangle made by Rachel and her shadow. Since Rachel is 5 feet tall and her shadow is 4 feet long, we have two similar triangles with the ratio of height to shadow length being the same.
We can set up a proportion to find the height of the flagpole (let's call it H):
- Rachel's height / Rachel's shadow = Flagpole height / Flagpole shadow
- 5 ft / 4 ft = H / 18 ft
By cross-multiplying to solve for H, we get:
- 4 ft * H = 5 ft * 18 ft
- H = (5 * 18) / 4
- H = 22.5 feet
Therefore, the flagpole is 22.5 feet tall.