Question

A triangle has side lengths of 34 in., 28 in., and 42 in. Is the triangle acute, obtuse, or right?

Answer 1

My guess is obtuse, but I'm not sure.

Answer 2

If \(\rm (longest~side)^2 = (one ~leg)^2 + (other~leg)^2\), then right.

If \(\rm (longest~side)^2 > (one ~leg)^2 + (other~leg)^2\), then obtuse.

If \(\rm (longest~side)^2 < (one ~leg)^2 + (other~leg)^2\), then acute.

Answer 3

Compare a^2 + b^2 to c^2
If they're equal, it's right (Pythagorean thm)
If c^2 is greater than a^2 +b^2, it's obtuse
If c^2 is less than a^2 +b^2, it's acute

Answer 4

OK, then I think I'm right. I'll do the math first though.

Answer 5

\[28\times28=784\]\[34\times34=1156\]\[784+1156=1940\]\[\sqrt{1940}=44\]So it is obtuse.

Answer 6

Thank you @ParthKohli and @bernadettegu

Answer 7

\[42^2 = 1764\]and\[28^2 + 34^2 = 1940 \]Which one is greater?

Answer 8

The second one.

Answer 9

So look at the conditions I gave.

Answer 10

So because it's longer then the longest side squared, it's obtuse.

Answer 11

The conditions are simple... see again.

Answer 12

\[42^2 < 28^2 + 34^2\]that's all.

Answer 13

Ok I see. Thanks for actually teaching me.

Answer 14

Hmm, the answer you get is still not right.

Answer 15

If \(\rm (longest~side)^2 < (one ~leg)^2 + (other~leg)^2\), the acute.

Answer 16

Oh, I kept reading it backwards.

Answer 17

Ah, all right...

Answer 18

So it's acute not obtuse.

Answer 19

Right.

Answer 20

The correct answer is .
Acute