Difference between revisions of "2021 Fall AMC 10A Problems/Problem 17"
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==Solution== | ==Solution== | ||
| + | Since the pillar at <math>B</math> has height <math>9</math> and the pillar at <math>A</math> has height <math>10</math> and the solar panel is flat, the inclination from pillar <math>A</math> to pillar <math>B</math> would be <math>1</math>. Call the center of the hexagon <math>G</math>. Since <math>CG</math> is parallel to <math>BA</math>, <math>G</math> has a height of <math>13</math>. Since the solar panel is flat, <math>BGE</math> should be a straight line and therefore, E has a height of <math>9+4+4</math> = <math>\boxed {(D) 17}</math>. | ||
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| + | ~Arcticturn | ||
Revision as of 20:44, 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 
?
Solution
Since the pillar at has height and the pillar at has height and the solar panel is flat, the inclination from pillar to pillar would be 
. Call the center of the hexagon 
. Since 
is parallel to 
, has a height of 
. Since the solar panel is flat, 
should be a straight line and therefore, E has a height of 
= 
.
~Arcticturn
