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 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 feet from the mirror. using similar triangles, find the height of the flagpole to the nearest tenth of a foot. a triangle with base 12 feet and height 5 feet. a similar triangle with base 48 feet. a. 20 ft b. 38.4 ft c. 55 ft d. 25 ft

Answer 1

a. 20 ft

Explanation:

a mirror reflects the beams of light with the outgoing angle being the same as the incoming angle.

the fact that the flagpole and Michele both have a right angle where they intersect with the ground, makes both triangles having all 3 angles in common and therefore similar triangles :

the triangle

flagpole

distance flagpole to mirror

line of sight mirror to top of flagpole

and the triangle

Michele

distance Michele to mirror

line of sight mirror to Michele's eyes

being similar triangles means also that there is one common scaling factor for all pairs of correlated sides of the triangles.

so, we only need to find the scaling factor of one pair of correlated sides to calculate the lengths of the others.

we get one such pair as the ground distance from the mirror.

for the Michele triangle this is 12 ft.

for the flagpole triangle this is 48 ft.

to go from small to large we get the scaling factor

12 × f = 48

f = 48/12 = 4

therefore, the height of the flagpole is calculated

Michele × 4 = flagpole

5 × 4 = flagpole

flagpole = 20 ft.