Question

can the sides of a triangle have lengths of 15, 44, and 47? 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.
$15 + 44=59>47$, $15 + 47 = 62>44$, $44 + 47=91>15$. So, a triangle can be formed.

Step2: Determine the type of triangle

Use the Pythagorean - like inequality. Let $a = 15$, $b = 44$, and $c = 47$ (where $c$ is the longest side). Calculate $a^{2}+b^{2}$ and $c^{2}$.
$a^{2}+b^{2}=15^{2}+44^{2}=225 + 1936=2161$.
$c^{2}=47^{2}=2209$.
Since $a^{2}+b^{2}

Answer:

yes, obtuse