Question 573849: What are the following triangles with these lengths for sides? Are they right triangles, acute triangles, or obtuse triangles?
3, 4, 5
5, 8, 10
3, 4, 6
3, 5, 8
4, 5, 8
4, 5, 10
6, 8, 10
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
First check to see if you have a triangle at all. Add the two short dimensions. If the sum is STRICTLY GREATER THAN the long side, then you have a triangle and you can proceed. (If the sum of the two short sides is equal to the third side, then you have a straight line -- not a triangle. If the sum of the two short sides is less than the third side, then you have two short sides flapping around unable to meet in a third vertex.)
Square the measures of each of the sides and then sum the squares of the two short sides.
If the sum is equal to the square of the long side, then you have a right triangle.
If the sum is less than the square of the long side, then you have an obtuse triangle.
If the sum is greater than the square of the long side, then you have an acute triangle.
Example: 3, 4, 6: 3 + 4 = 7 > 6, hence a triangle. 3 squared is 9, 4 squared is 16. 9 plus 16 is less than 6 squared (36), so you have an obtuse triangle.
John
My calculator said it, I believe it, that settles it
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