Problem:
An architect is building a structure that will place vertical pillars at the vertices of regular hexagon , which is lying horizontally on the ground. The six pillars will hold up a flat solar panel that will not be parallel to the ground. The heights of the pillars at , and are 12,9 , and 10 meters, respectively. What is the height, in meters, of the pillar at ?
Answer Choices:
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Solution:
Let be the midpoint of . The pillars at and are 12 and 10 meters high, respectively, so the height of the panel at is 11 meters. Because is a triangle, is half of the side length of the hexagon. Therefore . It follows that the height of the panel at point is meters.
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The problems on this page are the property of the MAA's American Mathematics Competitions