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For a project in her Geometry class, Chee uses a mirror on the ground to measure the
height of her school's football goalpost. She walks a distance of 14.35 meters from the
goalpost, then places a mirror on flat on the ground, marked with an X at the center.
She then steps 1.4 meters to the other side of the mirror, until she can see the top of
the goalpost 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 goalpost? Round your answer to
the nearest hundredth of a meter.

Respuesta :

The geometry technique that Chee uses to find the height of the goalpost is the equal ratio of the corresponding sides of similar triangles.

Correct response:

  • The eight of the goalpost is approximately 16.91 meters.

Methods used to calculate the height

The length Chee is using the mirror to measure = The height of her school's football goalpost

The distance of the mirror from the goalpost = 14.35 meters

The distance on the other side of the mirror Chee steps to =  1.4 meters

The distance from her eyes to the ground = 1.65 meters

Required:

How tall is the goalpost.

Solution:

By using similar triangles relationships, we have;

[tex]\dfrac{1.65}{1.4} = \mathbf{\dfrac{Height \ of \ the \ goalpost, h}{14.35} }[/tex]

Which gives;

[tex]h = \dfrac{1.65}{1.4} \times 14.35 = 16.9125 \approx \mathbf{ 16.91}[/tex]

  • The height of the goalpost, h ≈ 16.91 meters

Learn more about similar triangles here:

https://brainly.com/question/10676220

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