Difference between revisions of "2021 Fall AMC 10A Problems/Problem 17"
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An architect is building a structure that will place vertical pillars at the vertices of regular hexagon <math>ABCDEF</math>, 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 pillars at <math>A</math>, <math>B</math>, and <math>C</math> are <math>12</math>, <math>9</math>, and <math>10</math> meters, respectively. What is the height, in meters, of the pillar at <math>E</math>? | An architect is building a structure that will place vertical pillars at the vertices of regular hexagon <math>ABCDEF</math>, 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 pillars at <math>A</math>, <math>B</math>, and <math>C</math> are <math>12</math>, <math>9</math>, and <math>10</math> meters, respectively. What is the height, in meters, of the pillar at <math>E</math>? | ||
| − | <math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math> | + | <math>\textbf{(A) 9} \qquad\textbf{(B) 6\sqrt{3}} \qquad\textbf{(C) 8\sqrt{3}} \qquad\textbf{(D) 17} \qquad\textbf{(E) 12\sqrt{3}}</math> |
Revision as of 19:00, 22 November 2021
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 pillars at 
, 
, and 
are 
, 
, and 
meters, respectively. What is the height, in meters, of the pillar at 
?
$\textbf{(A) 9} \qquad\textbf{(B) 6\sqrt{3}} \qquad\textbf{(C) 8\sqrt{3}} \qquad\textbf{(D) 17} \qquad\textbf{(E) 12\sqrt{3}}$ (Error compiling LaTeX. Unknown error_msg)
