PLEASE HELP!! WILL AWARD BRAINLIST TO WHOEVER HAS ALL THE CORRECT CALCULATIONS!
2 answers:
Law of cosine:
c² = a² +b² -2ab*cosC.
Because the triangle is equilateral a=b=c=x,
and we can write,
x²=x² +x² -2xx*cosC
x² =2x² -2x²* cos C
-x² = -2x²*cos C
cos C= 1/2,
so m∠C=60⁰.
Because all sides are equal, and across of the equal sides should be equal angles, all angles will be also equal and = 60⁰.
Using the law of cosines, set up the equation and solve:
s^2 = s^2 + s^2 - 2 (s) (s) (cos x)
s^2 = 2s^2 - 2s^2 cos x
-s^2 = - 2s^2 cos x
0.5 = cos x
60 = x
This shows that all angles in an equilateral triangle must equal 60 degrees.
<em>Hope this helps!</em>
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