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

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