A triangle has sides A, B, and C. Sides A and B are of lengths #3# and #1#, respectively, and the angle between A and B is #(7pi)/12 #. What is the length of side C?

1 Answer
Jun 27, 2017

Answer:

approximately (to 3 decimal places): #3.400#

Explanation:

The Law of Cosines tells us:
#color(white)("XXX")C^2=A^2+B^2-2ABcos(/_c)#
where #/_c# is the angle between #A# and #B# (i.e. the angle opposite side #C#)

#C^2=3^2+1^1-2 * 3 * 1 * cos((7pi)/12)#

#color(white)("XXX")=9+1- 6 * (-0.252914271)color(white)("xxx")#(calculator use for this and all points beyond)

#color(white)("XXX")=10+1.55291427#

#color(white)("XXX")=11.55291427#

#C=sqrt(11.55291427)#

#color(white)("XX")=3.398957821#