Question

can the sides of a triangle have lengths of 5, 6, and 8? if so, what kind of triangle is it? yes, acute yes, right yes, obtuse no

Explanation:

Step1: Check triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
$5 + 6=11>8$, $5 + 8 = 13>6$, $6+8 = 14>5$. So, a triangle can be formed.

Step2: Determine the type of triangle using the Pythagorean - related rule

Let $a = 5$, $b = 6$, and $c = 8$ (where $c$ is the longest side). If $a^{2}+b^{2}=c^{2}$, it's a right - triangle; if $a^{2}+b^{2}>c^{2}$, it's an acute - triangle; if $a^{2}+b^{2}Calculate $a^{2}+b^{2}=5^{2}+6^{2}=25 + 36=61$, and $c^{2}=8^{2}=64$.
Since $a^{2}+b^{2}=61<64 = c^{2}$, the triangle is obtuse.

Answer:

yes, obtuse