A triangle has sides A, B, and C. Sides A and B are of lengths #8# and #4#, respectively, and the angle between A and B is #(11pi)/12 #. What is the length of side C?

1 Answer
Dec 18, 2015

Answer:

#C ~= 11.9#

Explanation:

If we denote the angle between #A# and #B# as #/_C# (not to be confused with the side #C# opposite #/_C#)

The Law of Cosines tells us
#color(white)("XXX")C^2 = A^2+B^2 - 2AB*cos(/_C)#
#rArr#
#color(white)("XXX")C = sqrt(A^2+B^2 - 2AB*cos(/_C))#

We are told that
#color(white)("XXX")A=8#
#color(white)("XXX")B=4#
#color(white)("XXX")/_C = (11pi)/12#

Plugging these values into the formula gives
#color(white)("XXX")C=11.90878889#