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.

Answer 1

The correct answer is:

20 feet.

Explanation:

48 ft would be the measurement of the base of the right triangle formed by the flagpole and the ground. We are trying to find the height of the flagpole, which is the other leg of this right triangle.

The measurements we have for the second triangle are 5 and 12. Since she is 12 feet away from the mirror, the base of the triangle is 12. Her eye level is at 5 feet, so this is the height of the triangle.

Since we know these triangles are similar, we can use proportions to solve this. 48 is to 12 (base is to base) as the unknown height is to 5 (height is to height):

48/12 = x/5

Cross multiply:

48*5 = 12*x

240 = 12x

Divide both sides by 12:

240/12 = 12x/12

20 = x

The unknown height is 20 feet.

Answer 2

Using similar triangles:
12 : 5 = 48 : h
12 h = 48 * 5
12 h = 240
h = 240 : 12
h =20.0 ft
Answer: The height of the flagpole is 20.0 ft.