If the sides of a triangle are a, b and `sqrt(a^(2) + ab + b^(2))`, then find the greatest angle

Options

A. `60^(@)`
B. `90^(@)`
C. `120^(@)`
D. none of these

Explanation

Let ABC be the given triangle such that BC= a, CA =b and CA = `sqrt(a^(2)+b^(2)+ab)=c` (say)
Clearly, `cgta` and `cgtb`.
Then, C is the greatest angle of triangle ABC
Now,
`cosC=(a^(2)+b^(2)-c^(2))/(2ab)`
`rArrcosC=(a^(2)+b^(2)-(a^(2)+b^(2)+ab))/(2ab)=-1/2rArrC=120^(@)`