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The lengths of sides of triangle ABC are...

The lengths of sides of `triangle ABC` are a units, b units and `sqrt(a^2+ab+b^2)` units show that greatest angle of the triangle is`120^@`

Text Solution

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The correct Answer is:
`120^(@)`
Sides are `a, b, sqrt(a^(2) + ab + b^(2))`
Then the greatest side `c = sqrt(a^(2) + ab + b^(2))`
Let the angle opposite to the greatest side be C.
`rArr cos C = (a^(2) + b^(2) - (a^(2) + ab + b^(2)))/(2ab) = (-1)/(2)`
`rArr C = 120^(@)`
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