2021 Fall AMC 10A Problems/Problem 17
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