Question

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?

Answer 1

Yes, a 92.16 degree angle is greater than a 90 degree obtuse angle but not a right angle

Explanation:

To ave a right triangle the two smaller sides squared added together would have to equal the largest side. A^2 + B^2 = C^2

2.6^2 +8.1^2= 8.6^2

6.76 + 65.61 = 73.96

72.37 = 73.96 No

Answer 2

By the converse of the Pythagorean Theorem, if 8.6 ^2 = 8.1 ^2 + 2.6 ^2 , then the triangle is right. 73.96 is not equal to 72.37 so the triangle is not a right triangle.

8.6^2 is greater than (8.1^2 + 2.6^2) which means that the triangle is obtuse.
The obtuse angle is opposite the 8.6 side.