Question

c) 3, 5, 5
acute
right
obtuse
the segments do not form a triangle

Explanation:

Step1: Verify triangle validity

Check triangle inequality: $3 + 5 > 5$, $5 + 5 > 3$, $3 + 5 > 5$. All hold, so triangle exists.

Step2: Use law of cosines for largest angle

Largest side is 5. Let $a=3, b=5, c=5$. Calculate $\cos C = \frac{a^2 + b^2 - c^2}{2ab}$
$\cos C = \frac{3^2 + 5^2 - 5^2}{2\times3\times5} = \frac{9}{30} = 0.3$

Step3: Classify by cosine sign

Since $\cos C > 0$, angle $C$ is acute. All angles in isosceles triangle are acute.

Answer:

acute