How do you find out if a triangle is acute, right, or obtuse by just the side lengths?

Question

If a triangle has sidess 6, 8, and 10, is it acute, right, or obtuse?

Answer 1

It is a right triangle in the ratio of 3, 4, and 5.

You could use the Pythagorean Theorem to verify it's right
please give me best answer

Answer 2

A^2 + B^2 = C^2
let: A=6
B=8
C=10
then

6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 10^2

There for the triangle in the above question is a right angled triangle.

NOTE :
A^2 + B^2 < C^2 Then the triangle is obtuse.
A^2 + B^2 > C^2. Then the triangle is acute.

Answer 3

For the future:
a^2 + b^2 > c^2 is an acute triangle
a^2 + b^2 < c^2 is an obtuse triangle
a^2 + b^2 = c^2 is a right triangle
Remember that 'c' is always the largest side.

Yours is a pythagorean triple:
3(2) , 4(2), 5(2)...it is a 3,4,5; and, yes, to repeat the previous answer, it is a right triangle.

Answer 4

If a^2+b^2=c^2 the trianle is right.
Since 6^2+8^2 =10^2 the triangle is right.
If a^2+b^2> c^2, then the triangle is acute
If a^2+b^2 Note that the sum of any two sides of a triangle must be > than the 3rd side.

Answer 5

It is a right triangle. Right triangles are in multiples of 3, 4, and 5. 6, 8, and 10 is just twice the size of the regular 3, 4, and 5 triangle.

Answer 6

there's a fromula to check this one
cos A=(b^2+c^2-a^2)/2*b*
where a is included angle and a,b,c are given sie
like this find cos B,cos C and from there u have all the angles and from this u can find out whether the triangle is acute right or obtuse...........

Answer 7

It is a right triangle in the ratio of 3, 4, and 5.

You could use the Pythagorean Theorem to verify it's righteousness.
.

Answer 8

it is obtuse beacause it cant be right because two of the angles have to be the same lenght and it cant be acute.

Answer 9

it is a right triangle as 6,8 and 10 are pythogorian triplet.

Answer 10

it is definately right triangle because 6,8,10 are congruent to 3,4,5...from the pythagorean theorem