Question 1199591
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cos(A)/a = cos(B)/b = cos(C)/c
cos(A)/a = cos(B)/b
cos(A)/cos(B) = a/b


Use the law of sines to apply similar steps:
sin(A)/a = sin(B)/b = sin(C)/c
sin(A)/a = sin(B)/b
sin(A)/sin(B) = a/b


We can see that:
cos(A)/cos(B) = a/b
cos(A)/cos(B) = sin(A)/sin(B)
which can be rearranged into
sin(B)/cos(B) = sin(A)/cos(A)
tan(B) = tan(A)
B = A
A = B


Follow a similar chain of logic to conclude that B = C.


We have A = B and B = C, so A = C
All three angles are the same measure. 
A+B+C = 180
A+A+A = 180
3A = 180
A = 180/3
A = 60
Each angle is 60 degrees.
The triangle is equilateral.


Area of equilateral triangle with side length 's'
Area = 0.25*s^2*sqrt(3)
Area = 0.25*2^2*sqrt(3)
Area = sqrt(3)



Answer: <font color=red>C)  sqrt(3)</font>
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