Question

A triangle has sides A, B, and C. Sides A and B are of lengths `7` and `4`, respectively, and the angle between A and B is `pi/6`. What is the length of side C?

Answer 1

`C=sqrt(65-28sqrt3)=sqrt16.51~=4.06.`

Explanation:

We use Cosine-rule for `DeltaLMN : n^2=l^2+m^2-2*l*m*cos/_(l,m).`

`:. C^2=A^2+B^2-2A*B*cos/_(A,B)=49+16-56cos(pi/6)=65-56*(sqrt3/2)=65-28sqrt3~=65-48.49=16.51.`

`:. C=sqrt16.51~=4.06.`