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EXPLANATION:

Remember that: When we are classifying what kind of the angles the giveb triples are: We will use the pythagorean theorem.

• If a²+b² = c² , then it is right
• If a²+b² > c² , then it is acute
• If a²+b² < c² , then it is obtuse

SOLUTION:

1.  a² + b² = c²

   4² + 5² = 6²

  16 + 25 = 36

          41 > 36

» Therefore , it is acute

2.   a² + b² = c²

     7² + (7√3)² = 14²

         49 + 147 = 196

                 196 = 196

» Therefore , it is right

3.  a² + b² = c²

    8² + 8² = 11²

   64 + 64 = 121

         128 > 121

» Therefore , it is acute

4.  a² + b² = c²

   8² + 12² = 15²

  64 + 144 = 225

         208 < 225

» Therefore , it is obtuse

5.  a² + b² = c²

    9² + 40² = 4²

    81 + 1600 = 16

            1681 > 16

» Therefore , it is acute

ANSWER

1. Acute
2. Right
3. Acute
4. Obtuse
5. Acute