Given 6, 8, and 11 as the three sides of a triangle, classify it as one of the following: A. Acute
B. Right
C. Obtuse

9514 1404 393

  C. Obtuse

Step-by-step explanation:

The "form factor" I use for this is ...

  a^2 + b^2 - c^2 = 6^2 + 8^2 - 11^2 = 36 +64 -121 = -21

The value is negative, indicating an OBTUSE triangle.

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Additional comment

In this expression, 'a' and 'b' are the two shortest sides (in no particular order) and 'c' is the longest side. The interpretation is ...

  negative — obtuse

  zero — right

  positive — acute

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If you're familiar with Pythagorean triples, you know that the 3-4-5 right triangle triple can be doubled to give 6-8-10. The long side of 11 is longer than the hypotenuse for the right triangle, so would correspond to a largest angle greater than 90°. The 6-8-11 triangle would be OBTUSE.

11. G (6,4)

12. H (4,9)

13. I (0,7)

14. J (9,5)

15. K (3,3)

16. L (5,2)

Step-by-step explanation:

eh you know