2011/108) prove that sum of 2 sides of an euclidian triangle is greater than 3rd side

let the angles be A B C and opposite sides be a b c

we need to prove that a + b > c

we have A+B = 180-C

hence sin (A+B) = sin (180-C) = sin C

or sin A cos B + cos A sin B = sin C

as cos B < 1 and cos A < 1 we have (it is 1 at zero degree not possible)



sin A cos B + cos A sin B < sin A + sin B so sin C < sin A + sin B

as a/sin A = b/sin B = c/sin C we get c < a + b

proved