Question
Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked 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.
The image shows a diagram of the flagpole, mirror, and person.
A right triangle is drawn between the flagpole and mirror with the right angle at the base of the flagpole . The lower segment of the triangle is labeled 48 feet.
Another right triangle is formed between the person and the mirror. The segment between the mirror and person is labeled 12 feet. The height of the person is labeled 5 feet.
(1 point)
Responses
20 ft
20 ft
38.4 ft
38.4 ft
55 ft
55 ft
25 ft
25 ft
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To solve this problem, we can use similar triangles. Let's label the height of the flagpole as x.
In the right triangle formed by the flagpole and mirror, the ratio of the height of the flagpole to the distance from the flagpole to the mirror is the same as the ratio of the height of the person (5 feet) to the distance from the person to the mirror (12 feet).
So, we can set up the following proportion:
x/48 = 5/12
To find x, we can cross-multiply and solve for x:
12x = 48 * 5
12x = 240
x = 240/12
x = 20
Therefore, the height of the flagpole is 20 feet.