Question

The three sides of a triangle are 5 inches, 8 inches and 9 inches. What is the best description for this triangle.

acute

equiangular

obtuse

right

Answer 1

Here's a right triangle with legs of lengths 5 and 8.
Can you calculate x, the length of the hypotenuse?

Answer 2

Not so fast. Have you calculated x?

Answer 3

No, you are missing the point.

I created a right triangle. In my right triangle I purposely made one leg 5 and one leg 8. I didn't say the hypotenuse was 9. For my triangle, I need to find the hypotenuse. My triangle may not be the same as the problem's triangle, but by comparing the problem's triangle with mine, we can find out if the problem's triangle is acute, right or obtuse.

Answer 4

gtg, I'll be back in around 15-20 min

Answer 5

@hyntc
Why do you deserve a medal for giving a wrong answer?

Answer 6

@hyntc ya why?

Answer 7

@theatreliver
Do you want to find the correct answer to this problem?

Answer 8

yes please

Answer 9

Ok, let's continue where we left off.
I drew above a right triangle with legs 5 and 8.
Can you use the Pythagoras theorem and find the length of the hypotenuse?
a^2 + b^2 = c^2
Here, a is 5 and b is 8.
Can you find c, the hypotenuse?

Answer 10

@hyntc Why can't it be obtuse?

Answer 11

how do i find the hypotensue

Answer 12

is it 9?

Answer 13

a^2 + b^2 = c^2

Answer 14

The Pythagorean theorem:
\(a^2 + b^2 = c^2\)

Answer 15

a and b are the lengths of the legs. The legs are the sides that form the right angle.
c is the length of the hypotenuse.
We know a = 5 and b = 8.
Plug in 5 for a and 8 for b and square them and add them together. What do you get?

Answer 16

\(a^2 + b^2 = c^2\)

\(5^2 + 8^2 = c^2\)

What is the left side equal to?

Answer 17

9.43

Answer 18

Ok, the hypotenuse is approx. 9.43
That's good.
Now understand what is going on.
If you have a right triangle with one leg measuring 5 and one leg measuriing 8, the hypotenuse will measure approx. 9.43.

Answer 19

What do we have in your problem?
We have one side of 5 and one side of 8, but the third side is 9, not 9.43.
The first thing we can conclude is that it is definitely not a right triangle.

Answer 20

so then what do i do?

Answer 21

Another thing we know from the beginning is that it is not an equiangular triangle. An equiangular triangle has all angles congruent. In order for that to happen, all sides must also be congruent. Here the sides have 3 different lengths, so it's not equilateral or equiangular.

Answer 22

Now we figure it out with a drawing.

Answer 23

so its either acute or obtuse

Answer 24

Yes.

If the triangle were a right triangle, we'd have 5, 8, and 9.43 as sides.

Answer 25

The third side, though, is 9 instead of 9.43.
That means we need to "close up" a little the angle between the sides of length 5 and 8 to fit the smaller side of 9.

Answer 26

Since we had to "close up" the angle, the new angle must be less than 90 degrees.
Therefore, it is an acute triangle.
An acute triangle has 3 acute angles/