To determine which side of the triangle [tex]$ABC$[/tex] has the greatest length, we can use the fact that in any triangle, the side opposite the largest angle is the longest.
Given the information:
- [tex]$\angle A = 55^\circ$[/tex]
- [tex]$\angle B = 65^\circ$[/tex]
- [tex]$\angle C = 60^\circ$[/tex]
Let's identify the largest angle among [tex]$\angle A$[/tex], [tex]$\angle B$[/tex], and [tex]$\angle C$[/tex].
- [tex]$\angle A = 55^\circ$[/tex]
- [tex]$\angle B = 65^\circ$[/tex] (this is the largest angle)
- [tex]$\angle C = 60^\circ$[/tex]
Since [tex]$\angle B = 65^\circ$[/tex] is the greatest angle, the side opposite [tex]$\angle B$[/tex] will be the longest side in triangle [tex]$ABC$[/tex].
The side opposite [tex]$\angle B$[/tex] is [tex]$\overline{ AC }$[/tex].
Therefore, the side of the terrace with the greatest length is:
B. [tex]$\overline{ AC }$[/tex]
