Question

For a project in her Geometry class, Victoria uses a mirror on the ground to measure the height of her school's football goalpost. She walks a distance of 12.35 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.25 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 1.75 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter. H 1.75 m 1.25 m 12.35 m​

Answer 1

0.20 meters

Explanation:

To find the height of the goalpost, you can use similar triangles. The triangles formed by the top of the goalpost, Victoria's eyes, and the point on the ground where she stood are similar to the triangles formed by the top of the goalpost, the X on the mirror, and the point where she moved to.

Let

ℎ

h be the height of the goalpost. The ratio of corresponding sides in similar triangles is equal. Therefore:

h/1.25=(h+1.75)/12.35

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Now, solve for h:

h={1.25⋅(h+1.75)}/12.35

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Multiply both sides by 12.35:

12.35⋅h=1.25⋅(h+1.75)

Distribute on the right side:

12.35h=1.25h+2.1875

Subtract 1.25h from both sides:

11.1h=2.1875

Divide by 11.1 to solve for h:

h≈2.1875/11.1

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Now, calculate h:
h≈0.19716 meters

So, the height of the goalpost is approximately 0.20 meters.