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For a project in his Geometry class, Feng uses a mirror on the ground to measure the height of his school’s flagpole. He walks a distance of 8.65 meters from the flagpole, then places a mirror on flat on the ground, marked with an X at the center. He then steps 1.1 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 eyes to the ground to be 1.65 meters. How tall is the flagpole? Round your answer to the nearest hundredth of a meter.

Answer :

The height of the flagpole, found using the ratio of the sides of similar triangles is 12.975 meters

What are similar triangles?

Similar triangles are triangles  in which two angles of one triangle  are congruent to two angles in the other triangle, such that they have the same shape.

The parameters that can be used to find the height of the flagpole are;

Distance of the mirror from the flagpole = 8.65 meters

Distance of Feng on the other side of the flagpole = 1.1 meters

The height from Feng's eyes to the ground = 1.65 meters

According to the law of reflection, the angle of incident and the angle of reflection are the same

The angle made by Feng and the ground = Angle made by the flagpole and the ground = 90°

The triangle formed by the Feng and the flagpole are therefore similar by AA similarity postulate

The ratio of corresponding sides of similar triangles are the same, therefore;

[tex]\dfrac{1.65}{Height\, of \, the \, flagpole} = \dfrac{1.1}{8.65}[/tex]

[tex]Height\, of \, the \, flagpole = \dfrac{1.65}{1.1} \times 8.65 = 12.975[/tex]

Height of the flagpole = 12.975  meters

Learn more about similar triangles here:

https://brainly.com/question/14285697

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