Respuesta :

I think its acute
The A²+B²=C² would be a right triangle, but considering 6²+23²>28² (Then it is an acute triangle)

Answer:

The triangle has side lengths of 23 in, 6 in, and 28 in. is an obtuse triangle.

Step-by-step explanation:

Given : A triangle has side lengths of 23 in, 6 in, and 28 in.

To Classify: It as acute, obtuse, or right.

Solution:

Let 'c' be the longest side on the set of three numbers.


If [tex]c^2 = a^2+b^2[/tex], the triangle is right


If [tex]c^2 > a^2+b^2[/tex], the triangle is obtuse


If [tex]c^2 < a^2+b^2[/tex], the triangle is acute.

So, let a=6 , b=23 and c=28

Now we put the value in  [tex]c^2 = a^2+b^2[/tex] to check it is equal,greater or less.

LHS - [tex]c^2[/tex]

[tex](28)^2=784[/tex]

RHS -  [tex]a^2+b^2[/tex]

[tex](6)^2+(23)^2[/tex]

[tex]=36+529=565[/tex]

which means [tex]784 > 565[/tex]

i.e, LHS > RHS

So, the triangle is an obtuse.

Therefore, The triangle has side lengths of 23 in, 6 in, and 28 in. is an obtuse triangle.