A triangle has sides A, B, and C. Sides A and B are of lengths #1# and #3#, respectively, and the angle between A and B is #(5pi)/6 #. What is the length of side C?

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Answer 1 · 2018-03-29T10:30:37

c=3.66

#cos(C)=(a^2+b^2-c^2)/(2ab)#
or
#c=sqrt(a^2+b^2-2abcos(C))#

We know that the sides a and b are 1 and 3
We know the angle between them Angle C is #(5pi)/6#

#c=sqrt((1)^2+(3)^2-2(1)(3)cos((5pi)/6))#

#c=sqrt((1+9-6(sqrt3/2)#

#c=sqrt((10-3sqrt3/2)#

Enter into a calculator

#c=3.66#