Question

For a project in his Geometry class, Jevonte uses a mirror on the ground to measure

the height of his school's flagpole. He walks a distance of 10.85 meters from the
flagpole, then places a mirror on flat on the ground, marked with an X at the center.
He then steps 1.15 meters to the other side of the mirror, until he can see the top of
the flagpole clearly marked in the X. His partner measures the distance from his
to the ground to be 1.65 meters. How tall is the flagpole? Round your answer to the
eyes
nearest hundredth of a meter.
1.65 m
1.15 m
(Diagram is not to scale.)
10.85 m-

Answer 1

15.57 m

Explanation:

You want the height of a flagpole reflected in a mirror placed 10.85 m away to the eyes of a person 1.15 m from the mirror at a height of 1.65 m.

Similar triangles

The mirror ensures that the triangle between the mirror, the observer's eyes and the ground is similar to the triangle between the mirror, the top of the flagpole, and its base. This means the ratio of height to distance from the mirror is the same for both triangles:

height/(10.85 m) = (1.65 m)/(1.15 m)

height = (10.85 m)(1.65/1.15) ≈ 15.57 m

The height of the flagpole is about 15.57 meters.

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