A triangle has sides A, B, and C. Sides A and B are of lengths #6# and #1#, respectively, and the angle between A and B is #(7pi)/12 #. What is the length of side C?

1 Answer
Jul 25, 2016

Answer:

#C=sqrt(37+3(sqrt(6)-sqrt(2))#

Explanation:

You can apply the theorem of Carnot, by which you can calculate the lenght of the third side C of a triangle if you know two sides, A and B, and the angle #hat (AB)# between them:

#C^2=A^2+B^2-2*A*B*cos(hat(AB))#

Then #C^2=6^2+1^2-2*6*1*cos((7pi)/12)#

#C^2=36+1-12*(-1/4(sqrt(6)-sqrt(2)))#

#=37+3(sqrt(6)-sqrt(2))#

#C=sqrt(37+3(sqrt(6)-sqrt(2))#