Question
For a project in her Geometry class, Sadie uses a mirror on the ground to measure the height of
her school’s football goalpost. She walks a distance of 6.45 meters from the goalpost, then
places a mirror flat on the ground, marked with an X at the center. She then walks 4.65 more
meters past the mirror, so that when she turns around and looks down at the mirror, she can
see the top of the goalpost clearly inarked in the X. Her partner measures the distance from her
eyes to the ground to be 1.55 meters. How tall is the goalpost? Round your answer to the
nearest hundredth of a meter.
her school’s football goalpost. She walks a distance of 6.45 meters from the goalpost, then
places a mirror flat on the ground, marked with an X at the center. She then walks 4.65 more
meters past the mirror, so that when she turns around and looks down at the mirror, she can
see the top of the goalpost clearly inarked in the X. Her partner measures the distance from her
eyes to the ground to be 1.55 meters. How tall is the goalpost? Round your answer to the
nearest hundredth of a meter.
Ask by Klein Mathis. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The goalpost is 2.15 meters tall.
Solution
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Mind Expander
To find the height of the goalpost, we can use similar triangles. Sadie’s total distance from the goalpost to her eyes when looking into the mirror is the sum of the distance from the goalpost to the mirror (6.45 meters) and the distance she walked past the mirror (4.65 meters), which totals 11.10 meters.
The ratio of Sadie’s eye level (1.55 meters) to the height of the goalpost (h) corresponds to the ratio of her distance from the goalpost (11.10 m) to her distance from the mirror (6.45 m).
Setting up the proportion:
1.55 / h = 6.45 / 11.10
1.55 / h = 6.45 / 11.10
Cross-multiplying gives:
1.55 * 11.10 = h * 6.45
1.55 * 11.10 = h * 6.45
Now, solving for h:
h = (1.55 * 11.10) / 6.45 ≈ 2.65 meters.
h = (1.55 * 11.10) / 6.45 ≈ 2.65 meters.
So, rounding to the nearest hundredth, the height of the goalpost is approximately 2.65 meters.
Understanding how the concept of similar triangles works can help in grasping various topics in Geometry. By realizing that angles formed by lines to the top of the goalpost create similar triangles, you can solve a multitude of real-life problems using geometric principles!
This technique is not just limited to goalposts or mirrors. You can apply the same method in various situations, such as measuring the height of a tree or a building, where direct measurement is impractical. All you need are your measuring tools and a reflective surface!
