Download Solution for Centroid of Equilateral Triangle Solution using Unit

Solution for Centroid of Equilateral Triangle
GES 131-008
Fall 2004
Solution using Unit Circle
If you remember the coordinates for three
common angles on a unit circle (see figure to
right), then this problem is easily solved.
1/3
(0,1)
⎛1 3⎞
⎜
⎟
⎜2 2 ⎟
⎝
⎠
y
⎛ 2 2⎞
⎟
⎜
,
⎜ 2 2 ⎟
⎠
⎝
⎛ 3 1⎞
⎜
, ⎟
⎜ 2 2⎟
⎠
⎝
π
π
3
4
π
6
x
Unit Circle
The angle at each vertex in the triangle is
equal to the total of all the angles in a
triangle divided by 3,
180o
angle at vertex =
= 600
3
The angle formed by drawing a line from
the vertex to the midpoint of the opposite
side = 60o / 2 = 30o.
30o = 1/6 of a half circle; therefore 30o =
π/6.
tan 30 o = tan
π
6
=
y
a/2
3
2
From the unit circle: tan =
= 3
1
6
2
y
a
Therefore: 3 =
, y=
a/2
2 3
π
30o
y
a/2
(1,0)