Question

For a project in her Geometry class, Madelyn uses a mirror on the ground to measure
the height of her school's flagpole. She walks a distance of 8.75 meters from her
school, then places a mirror on flat on the ground, marked with an X at the center.
She then steps 1.7 meters to the other side of the mirror, until she can see the top of
the flagpole clearly marked in the X. Her partner measures the distance from her eyes
to the ground to be 1.65 meters. How tall is the flagpole? Round your answer to the
nearest hundredth of a meter.
1.65 m
1.
1.7 m
-8.75 m

Answer 1

An image is always formed at the back of a mirror. Thus, the appropriate option is D. -8.75 m. The flagpole is 8.75 m tall.

Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;

Tan θ = $\frac{opposite}{adjacent}$

          = $\frac{1.65}{1.7}$

Tan θ = 0.9706

θ = $Tan^{-1}$ 0.9706

  = $44.2^{o}$

θ = $44.2^{o}$

Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;

Tan θ = $\frac{opposite}{adjacent}$

         = $\frac{h}{8.75}$

0.9706 = $\frac{h}{8.75}$

h = 0.9706 x 8.75

  = 8.49275

h = 8.5 m

Since the image is formed at the back of the mirror, then the flagpole is 8.5 m.

Therefore the appropriate answer is option D. -8.75 m

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Answer 2

Answer:

10.77

Step-by-step explanation:

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