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A person is standing on top of a six foot platform, looking down into a mirror. The person can see the top of the flagpole in the mirror. How tall is the flagpole? Use similar triangles to solve for the height. Explain your procedure.

A Person Is Standing On Top Of A Six Foot Platform Looking Down Into A Mirror The Person Can See The Top Of The Flagpole In The Mirror How Tall Is The Flagpole class=

Sagot :

Answer:  The flagpole is 16 feet tall

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Explanation:

The small markings for the angles in the diagram help us see how the angles pair up and how those pairs are congruent.

The square angle markers indicate we have 90 degree angles (aka right angles). That's one pair of congruent angles.

The other pair are the angles marked with small curves. We don't need to worry about the angle measure of these. All we care about is we have a second congruent pair of angles.

Having 2 sets of congruent angles allows us to use the AA (angle angle) similarity theorem.

The similar triangles allow us to set up the proportion below and isolate x.

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Let's solve for x.

6/x = 4.5/12

6*12 = x*4.5

72 = 4.5x

4.5x = 72

x = 72/(4.5)

x = 16

The flagpole is 16 feet tall.

This is somewhere between a 1 and 2 story building in terms of height.

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