MathDB
A weird solar panel

Source: 2021 AMC 10A (Fall) #17

November 11, 2021

Problem Statement

An architect is building a structure that will place vertical pillars at the vertices of regular hexagon ABCDEFABCDEF, 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 AA, BB, and CC are 12,9,12,9, and 1010 meters, respectively. What is the height, in meters, of the pillar at EE?
<spanclass=latexbold>(A)</span>9<spanclass=latexbold>(B)</span>63<spanclass=latexbold>(C)</span>83<spanclass=latexbold>(D)</span>17<spanclass=latexbold>(E)</span>123<span class='latex-bold'>(A) </span>9\qquad<span class='latex-bold'>(B) </span>6\sqrt3\qquad<span class='latex-bold'>(C) </span>8\sqrt3\qquad<span class='latex-bold'>(D) </span>17\qquad<span class='latex-bold'>(E) </span>12\sqrt3