Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obt
1 answer:
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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<em>Additional comment</em>
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°
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