Question

A triangle has side lengths of 23 in, 6 in, and 28 in. Classify it as acute, obtuse, or right.

Answer 1

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 2

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 $c^2 = a^2+b^2$, the triangle is right

If $c^2 > a^2+b^2$, the triangle is obtuse

If $c^2 < a^2+b^2$, the triangle is acute.

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

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

LHS - $c^2$

$(28)^2=784$

RHS -  $a^2+b^2$

$(6)^2+(23)^2$

$=36+529=565$

which means $784 > 565$

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.