Question

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?

Answer 1

`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))`