A triangle has side lengths of 23 in, 6 in, and 28 in. Classify it as acute, obtuse, or right.
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 \(c^2 = a^2+b^2\), 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.