A triangle has sides A, B, and C. Sides A and B are of lengths #2# and #7#, respectively, and the angle between A and B is #(5pi)/12 #. What is the length of side C?

1 Answer
Apr 6, 2017

Answer:

#C=7#

Explanation:

The length of #A# is #2#

The length of #B# is #7#

The angle between #A# and #B# is #/_c=(5pi)/12#

Now to the Law of Cosines

#C^2=A^2+B^2-2AB*cosc#

#C=sqrt(A^2+B^2-2AB*cosc#

We will simply substitute the values we have and find the length of #C#

#C=sqrt(2^2+7^2-2(2)(7)*cos(5pi)/12#

#color(red)(NOTE):# Your calculator should be in radian mode when computing this. If you cannot change it to rad then change the angle to degrees and compute it.

#(5cancelpi)/12xx180^0/cancelpi=75^0#

#C=sqrt(4+49-2(14)*cos(5pi)/12#, if your calculator is in #color(red)(radian)# mode

#C=sqrt(4+49-2(14)*cos75^0#, if your calculator is in #color(red)(degree)# mode

#C=6.76~~7#