To determine which side of a triangle has the greatest length, we look at the measures of the angles of the triangle. In any triangle, the side opposite the largest angle is the longest side.
Given:
- [tex]\(\angle A = 55^\circ\)[/tex]
- [tex]\(\angle B = 65^\circ\)[/tex]
- [tex]\(\angle C = 60^\circ\)[/tex]
First, compare the angles:
- [tex]\(\angle B = 65^\circ\)[/tex] (largest angle)
- [tex]\(\angle C = 60^\circ\)[/tex]
- [tex]\(\angle A = 55^\circ\)[/tex]
Since [tex]\(\angle B\)[/tex] is the largest angle in the triangle, the side opposite [tex]\(\angle B\)[/tex] will be the longest side.
In triangle [tex]\(ABC\)[/tex]:
- The side opposite [tex]\(\angle A\)[/tex] is [tex]\(\overline{BC}\)[/tex].
- The side opposite [tex]\(\angle B\)[/tex] is [tex]\(\overline{AC}\)[/tex].
- The side opposite [tex]\(\angle C\)[/tex] is [tex]\(\overline{AB}\)[/tex].
Therefore, the side opposite to [tex]\(\angle B\)[/tex] is [tex]\(\overline{AC}\)[/tex].
Hence, the correct answer is:
A. [tex]\(\overline{BC}\)[/tex]
