Question

A triangle has sides A, B, and C. Sides A and B are of lengths `3` and `9`, respectively, and the angle between A and B is `pi/6`. What is the length of side C?

Answer 1

`C=3root2(10-3root2(3))`

Explanation:

By applying the cosinus theorem, we have
`C=root2(A^2+B^2-2*A*B*cos(pi/6)`
`C=root2(3^2+9^2-2*3*9*cos(pi/6))`
`C=root2(90-54*root2(3)/2)=`
`C=3root2(10-3root2(3))`