Answer:
An obtuse triangle is a triangle that has one angle measuring more than 90 degrees. In a triangle, the sum of the angles is always 180 degrees. If two sides of a triangle have lengths "a" and "b," and if we know that angle C (opposite side C) is obtuse, then we can use the law of cosines to determine the possible range of values for the length of the third side, "c":
c^2 = a^2 + b^2 - 2ab * cos(C)
If C is obtuse, then cos(C) will be negative. In this case, the value of c^2 will be larger than a^2 + b^2, meaning c (the third side) will be longer than the sum of the other two sides. This is not possible according to the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side.
Therefore, if you have a triangle with sides of lengths "a" and "b," it cannot be an obtuse triangle if the sum of the lengths of these two sides is less than or equal to the length of the third side. In other words, the triangle inequality must hold for all three sides of the triangle for it to be a valid triangle.
In summary, if you have a triangle with sides of length "a" and "b," and the sum of these two sides is less than or equal to the length of the third side, then it cannot be an obtuse triangle. It would either be an acute triangle (all angles less than 90 degrees) or not a triangle at all, depending on the lengths of the sides.