Question

Michele wanted to measure the height of her school's flagpole. She placed a mirror on the ground 50 feet from the flagpole and then walked backward until she was able to see the top of the flagpole in the mirror. Her eyes were 5.5 feet above the ground, and she was 10 feet from the mirror. Using similar triangles, find the height of the flagpole.

Answer 1

By using similar triangles, Michele determined the height of her school's flagpole. She used the proportions of her eye height and the distances from the mirror to herself and the flagpole. The flagpole's height was calculated to be 27.5 feet.

Step-by-step explanation:

Michele can calculate the height of her school's flagpole by using the principles of similar triangles. The situation described creates two right triangles: one from Michele's eyes to the mirror and then to her feet, and another from the top of the flagpole to the mirror and then to the base of the flagpole. We know that the distance from Michele's eyes to the ground is 5.5 feet and the distance from the mirror to her eyes is 10 feet. The distance from the mirror to the flagpole is given as 50 feet.

To find the flagpole's height, we set up a proportion using the corresponding sides of the two triangles:

1. Let x be the height of the flagpole.
2. The ratio of Michele's eye height to the distance from her eyes to the mirror is 5.5 feet / 10 feet.
3. The ratio of the flagpole's height to the distance from the mirror to the flagpole is x feet / 50 feet.
4. Set the two ratios equal to each other to get the proportion: 5.5 / 10 = x / 50.
5. Using cross-multiplication, we get 5.5 * 50 = 10 * x.
6. After simplifying, we find x = 27.5 feet.

Therefore, the flagpole's height is 27.5 feet.