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Answer:
see attached
Step-by-step explanation:
For this exercise, it is convenient to define a, b, c as the side lengths in increasing order. (The only thing that really matters is that c=longest.)
Below, we have used a spreadsheet to do the calculations.
When a^2+b^2 > c^2, the triangle is acute. For "<", the triangle is obtuse. For "=", the Pythagorean theorem is satisfied and the triangle is a right triangle.
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Additional comment
The measure of the largest angle in the triangle is ...
α = arccos((a²+b²-c²)/(2ab))
Knowing that the cosine is negative for angles larger than 90° helps me remember how the relationship of a²+b² to c² relates to the shape of the triangle.
