Final answer:
By equating the ratios of similar triangles formed by the goalpost, the mirror, and Lauren's eye level, we find that the height of the goalpost is approximately 5.83 meters. This is not one of the provided options, suggesting a potential error in the question options or calculation.
Step-by-step explanation:
To determine the height of the football goalpost using the mirror method, Lauren essentially formed two similar right triangles. The first right triangle is between the top of the goalpost, the point on the ground directly below it, and the mirror. The second triangle is between Lauren's eyes, the point on the ground where she is standing, and the mirror.
Since the triangles are similar, the ratios of corresponding sides are equal. This means that the ratio of the height of the goalpost to the distance from the goalpost to the mirror is equal to the ratio of the height of Lauren's eyes to the distance from her eyes to the mirror.
Using this proportion, we can set up the following equation:
Height of Goalpost / Distance from Goalpost to Mirror = Height of Eyes / Distance from Eyes to Mirror
By plugging in the given values:
Height of Goalpost / 12.35 m = 1.35 m / 2.85 m
To solve for the Height of Goalpost, we cross-multiply and divide:
Height of Goalpost = (1.35 m * 12.35 m) / 2.85 m
Height of Goalpost ≈ 5.83 m
Therefore, the height of the goalpost, rounded to the nearest hundredth of a meter, is approximately 5.83 meters, which is not one of the options provided in the question. This indicates that the height has to be recalculated if parentheses are not correctly used or the given answer options are incorrect.