Question

Michele wanted to measure the height of her school's flagpole. She placed herself on the ground 35 ft from the flagpole and then walked backwards 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 ft away from the mirror. Using similar triangles, find the height of the flagpole to the nearest foot.

1) 20 ft
2) 38.4 ft
3) 55 ft
4) 25 ft

Answer 1

Using similar triangles and proportions, the height of the flagpole can be found to be 38.4 feet.

Step-by-step explanation:

To find the height of the flagpole, we can use similar triangles. The height of the mirror is half the height of the person, so it is 5/2 = 2.5 feet. Now, we can set up a proportion using the similar triangles:

(Height of flagpole + height of person) / 35 = height of mirror / 12

Substituting the known values, we get:

(Height of flagpole + 5) / 35 = 2.5 / 12

Cross multiplying and solving for the height of the flagpole, we get:

Height of flagpole = (2.5 / 12) * 35 - 5 = 38.4 feet