# 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.**