To determine which side of the triangular rooftop terrace [tex]$\triangle ABC$[/tex] modeled by the angles given has the greatest length, we can use the relationship between the angles and the sides in a triangle.
In any triangle, the side opposite the greatest angle will be the longest side. This is based on the fundamental property of triangles where larger angles are opposite longer sides.
Given the measures of the angles:
- [tex]$\angle A = 55^\circ$[/tex]
- [tex]$\angle B = 65^\circ$[/tex]
- [tex]$\angle C = 60^\circ$[/tex]
We observe that:
- [tex]$\angle A = 55^\circ$[/tex]
- [tex]$\angle B = 65^\circ$[/tex]
- [tex]$\angle C = 60^\circ$[/tex]
Among these angles, [tex]$\angle B = 65^\circ$[/tex] is the greatest.
The side opposite [tex]$\angle B$[/tex] is side [tex]$\overline{AC}$[/tex].
Therefore, the side with the greatest length in triangle [tex]$\triangle ABC$[/tex] is [tex]$\overline{AC}$[/tex].
So the correct answer is:
B. [tex]$\overline{AC}$[/tex]
