Suppose someone tells you that she has a triangle with sides having lengths 2.6, 8.1, and 8.6. Is this a right triangle? Why or why not? Is there an angle in the triangle larger than 90 degree?

First you check for Pythagoras' Theorem.

Is 8.6² = 8.1² + 2.6²?

8.1² + 2.6² = 65.61 + 6.76 = 72.37

8.6² = 73.96

8.1² + 2.6² ≠ 8.6²

Since Pythagoras' Theorem is not satisfied it is not a right angled triangle.

The longest side is 8.6, let's find the angle facing the longest side 8.6.

By cosine formula CosA = (b² + c² - a²) / (2bc)

CosA = (2.6² + 8.1² - 8.6²) / (2*2.6*8.1) = - 1.59/42.12 = - 0.0377

A = Cos inverse (-0.0377) = 92.1 degrees

So there is an angle is greater than 90 degrees.