Michele wanted to measure the height of her school's flagpole. She placed a mirror on the ground 60 ft from the flag pole, then walked backward until she was able to see the top of the pole in the mirror. Her eyes are 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flag pole to the nearest tenth of a foot.
(1 point)
Responses
55 ft
55 ft
38.4 ft
38.4 ft
25 ft
25 ft
20 ft
Let's use similar triangles to solve this problem.
Let h be the height of the flagpole.
The distance from Michele's eyes to the top of the flagpole is h + 5 (her height plus the height of her eyes).
The distance from Michele's eyes to the mirror is 60 ft + 12 ft (the distance from the mirror to the flagpole plus the distance from Michele to the mirror).
We can set up the following proportion:
(h + 5) / 12 ft = h / 60 ft
Cross multiplying, we get:
60(h + 5) = 12h
Simplifying, we have:
60h + 300 = 12h
48h = -300
h = -300/48 = -6.25 ft
Since we are looking for the height in positive values, we can disregard the negative sign.
Therefore, the height of the flagpole is approximately 6.25 feet.
None of the given answer choices match the calculated value.