SOLUTION: Does the set of numbers: 17, 19, 35 make an obtuse angle? And what about 16, 17, 31? I got obtuse for both of them but my answer choices doesn't contain that. It says one has to be

Algebra ->  Pythagorean-theorem -> SOLUTION: Does the set of numbers: 17, 19, 35 make an obtuse angle? And what about 16, 17, 31? I got obtuse for both of them but my answer choices doesn't contain that. It says one has to be      Log On


   

Question 840865: Does the set of numbers: 17, 19, 35 make an obtuse angle? And what about 16, 17, 31? I got obtuse for both of them but my answer choices doesn't contain that. It says one has to be obtuse and one does not make a triangle? So which is it? Am I going crazy or the problem's wacky? Thank you~ Have a nice day (:
Answer by KMST(5397) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct.
Wacky. There must be a typo.
Maybe one of the 17's was supposed to be 11 instead.
To make a triangle, the sum of the lengths of 2 sides must be greater than the length of the third side.
17%2B19=36%3E35 and 16%2B17=33%3E31
Both sets of side lengths make triangles, and since for each set the longest side's length is so close to the sum of the other sides' lengths, you would expect them to be obtuse.

I am sure you compared the squares:
16%5E2%2B17%5E2=256%2B289=445%3C961=31%5E2
17%5E2%2B19%5E2=289%2B361=650%3C1225=35%5E2 .
That proves they are obtuse.
That is a lot of calculation, but it is expected if the problem asks to "show your work".

Can we prove it without much calculation?
That would help in a timed multiple choice test.
An isosceles right triangle with a leg length of 20, would have a hypotenuse with length
sqrt%282%2A20%5E2%29=20sqrt%282%29%3C20%2A1.5=30 .
That means that an isosceles triangle with two side lengths of 20, and a third side length of 30 or more would be obtuse.
That means that a triangle with two side lengths shorter than 20, and a third side length longer than 30 is obtuse too.