Michele wanted to measure the height of her school's flagpole. She placed a mirror on the ground 48 feet from the flagpole, then waked backward until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground, and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.
(1 point)
Responses
25 ft
25 ft
55 ft
55 ft
20 ft
20 ft
38.4 ft
38.4 ft
To solve this problem, we can set up a proportion using the similar triangles formed by Michele, the mirror, and the flagpole.
Let's let h be the height of the flagpole.
In the small triangle formed by Michele's eyes, the mirror, and the top of the flagpole, we have the following proportions:
h / (h + 5) = 48 / 12
Cross multiplying, we get:
12h = 48(h + 5)
Expanding the equation, we get:
12h = 48h + 240
Subtracting 48h from both sides, we get:
-36h = 240
Dividing both sides by -36, we get:
h = -240 / -36
Simplifying, we get:
h ≈ 6.7
Therefore, the height of the flagpole is approximately 6.7 feet.