Question

A triangle has side lengths 20, 21, and 40. Is the triangle acute, right or obtuse?
Answer
a. Acute
b. Obtuse
c. Right
d. Not a triangle

Answer 1

Can someone explain how to do that?

Answer 2

it is a triangle because any 2 lines is longer than the other line
20 + 21 = 41 - just 1 longer than 40
- so it will be obtuse

Answer 3

ok thanks now i understand

Answer 4

looks something like

Answer 5

yw

Answer 6

Hint:
a^2 + b^2 > c^2 = acute
a^2 + b^2 < c^2 = obtuse

Answer 7

You can't use @cwrw238's method because any two sides of a triangle is always longer than the third side no matter what

Answer 8

your equations are of course correct hero but this as an extreme case so my method did work in this scenario

Answer 9

How is this an extreme case? It's just a triangle like any other. It will either be acute or obtuse.

Answer 10

Your method is indeed flawed and not the logic that is used to solve these

Answer 11

hmmm

Answer 12

Okay for example, you have sides 6,7,8

Answer 13

could you help with me latest problem?

Answer 14

According to your method, since 6 + 7 = 13 and 13 > 8 , then that means the triangle is obtuse right? @cwrw238

Answer 15

But it is in fact acute

Answer 16

no - the 21 and 20 sides have a sum which is only 1 more than the 40 and they are only about half the length of 40 so it is obvious that the angle as drawn will be obtuse!!
thats what i meant when i said it was an extreme case.

Answer 17

Either way, your method is inconsistent and should not be used to determine these. I'm pretty sure I can find a counter example to your claim

Answer 18

yours is the correct general method but in this case I just used plain common sense - its as simple as that