Question

Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right 7,15,21

Answer 1

9514 1404 393

Answer:

  obtuse triangle

Step-by-step explanation:

The two shortest sides are 7, 15. Their sum is 7+15 = 22, which is longer than the longest side, so these lengths will form a triangle.

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The "form factor" can be computed to be ...

  a^2 +b^2 -c^2 . . . . . where c = longest side

This value is ...

  7^2 +15^2 -21^2 = 49 +221 -441 = -167

This negative value indicates the largest angle is more than 90°, so the triangle is obtuse.

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Additional comment

This "form factor" has the same sign as the cosine of the largest angle. The cosine is negative for angles greater than 90°. The cosine of the angle is ...

  "form factor"/(2ab) = -167/210

  largest angle = arccos(-167/210) ≈ 142.678°