What is the height of the flagpole?

Question

person is trying to find the height of a flagpole or AB. This person is 1.5 m tall and is standing at DC. A mirror is placed at point M. This mirror is 6 m away from the person and 120 m away from the flagpole. Angles BMA and DMC are congruent. Find the height of the flagpole or BA.

Answer 1

Hi Jniya, thanks for the question!

Visually we’d have the flagpole at the far left, the mirror at the far right, and the person between them. We’ll let X be the height of the flagpole.

Angles BMA and DMC are congruent, and the triangles formed by the points BMA and DMC are what we’d call similar to each other. That means that the ratios of the two triangles’ side lengths are the same.

For example, the ratio of BM (distance from bottom of flagpole to mirror) to DM (distance from bottom of person to mirror) is 120/6 = 20. The ratio of BA (height of flagpole) to DC (height of person) is X/1.5.

Since the ratios have to be the same, that means 20 = X/1.5. When we solve that equation, X = 30 meters.

Good luck and please let me know if I can be more helpful.

Joe

Answer 2