How many obtuse angles can an equilateral triangle have?
1 Answer
Nov 24, 2015
None. An equilateral triangle has three equal sides, and thus three equal angles.
We can prove this using the law of cosines with the SSS case.
#a = b = c#
#c^2 = a^2 + b^2 - 2abcos/_C#
becomes
#a^2 = a^2 + a^2 - 2a*a*cos/_A#
#-a^2 = -2a^2cos/_A#
#1 = 2cos/_A#
#1/2 = cos/_A#
#color(blue)(/_A = 60^@)#
Since only one side
Acute angles cannot be greater than
Therefore, with three acute angles, there are no obtuse angles.