Question

can the sides of a triangle have lengths of 0.6, 0.8, and 1? if so, what kind of triangle is it? yes, acute yes, right yes, obtuse no

Explanation:

Step1: Check triangle - inequality

Check if the sum of any two sides is greater than the third side.
$0.6 + 0.8=1.4>1$, $0.6 + 1 = 1.6>0.8$, $0.8 + 1=1.8>0.6$. So, a triangle can be formed.

Step2: Determine the type of triangle

Use the Pythagorean - theorem and its converse. Let $a = 0.6$, $b = 0.8$, and $c = 1$. Calculate $a^{2}+b^{2}$ and $c^{2}$.
$a^{2}=0.6^{2}=0.36$, $b^{2}=0.8^{2}=0.64$, then $a^{2}+b^{2}=0.36 + 0.64 = 1$. And $c^{2}=1^{2}=1$. Since $a^{2}+b^{2}=c^{2}$, by the converse of the Pythagorean theorem, the triangle is a right - triangle.

Answer:

B. yes, right