Question

can the sides of a triangle have lengths of 16, 30, and 34? 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.
$16 + 30=46>34$, $16 + 34 = 50>30$, $30+34 = 64>16$. So, a triangle can be formed.

Step2: Determine the type of triangle

Use the Pythagorean - theorem converse. Let $a = 16$, $b = 30$, and $c = 34$. Check if $a^{2}+b^{2}=c^{2}$.
$a^{2}=16^{2}=256$, $b^{2}=30^{2}=900$, $c^{2}=34^{2}=1156$.
$a^{2}+b^{2}=256 + 900=1156=c^{2}$.

Answer:

B. yes, right