9514 1404 393
Answer:
right
Step-by-step explanation:
If you're going to be in the business of classifying triangles based on side lengths, it can be useful to know there is a "form factor" that can help. For sides a, b, c, with long side 'c', it is computed as ...
f = a² + b² - c²
It has the following interpretation with respect to triangle shape:
f > 0 . . . acute
f = 0 . . . right
f < 0 . . . obtuse
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In this case, we have ...
16² +63² -65² = 256 +3969 -4225 = 0
The triangle is a right triangle.
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Additional comment
When the triangle is a right triangle, this is equivalent to a statement of the Pythagorean theorem: c² = a² + b².
For triangles of other shapes, the interpretation is consistent with the Law of Cosines. When the form factor is divided by 2ab, the result is the cosine of the largest angle. That is why >0 means acute and <0 means obtuse.
