Is a triangle with sides 6 8 10 obtuse?

Let us state some facts. If the degree measure of the angle α is greater than 90 and less than 180 degrees, then such an angle is called an obtuse angle, that is, if 90 ° <α <180 °. If the angle α lies on the II coordinate quarter, that is, if 90 ° <α <180 °, then cos α <0.
If a triangle is obtuse, then only one corner of this triangle can be obtuse, and the other two corners are sharp. In addition, in any triangle, there is a larger angle opposite the larger side.
Among the sides given in the task (a = 6, b = 8 and c = 10) of the triangle, the largest side is c = 10. Calculate the cosine of the angle C, which lies opposite side c. By the cosine theorem, c^2 = a^2 + b^2 – 2 * a * b * cos∠C, whence cos∠C = (c ^ 2 – a ^ 2 – b ^ 2) / (2 * a * b) = (10 ^ 2 – 6 ^ 2 – 8 ^ 2) / (2 * 6 * 8) = (100 – 36 – 64) / 96 = 0/96 = 0. This means that ∠C = 90 ° (that is, the angle С is a straight line ). If a triangle has one right angle, then it is not obtuse; he is a right-angled triangle.
Answer: No.