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A building has a triangular rooftop terrace modeled by triangle [tex]\(ABC\)[/tex]. In triangle [tex]\(ABC\)[/tex]:
- The measure of [tex]\(\angle A\)[/tex] is [tex]\(55^\circ\)[/tex].
- The measure of [tex]\(\angle B\)[/tex] is [tex]\(65^\circ\)[/tex].
- The measure of [tex]\(\angle C\)[/tex] is [tex]\(60^\circ\)[/tex].

Which side of the terrace has the greatest length?
A. [tex]\(\overline{AC}\)[/tex]
B. Cannot be determined
C. [tex]\(\overline{AB}\)[/tex]
D. [tex]\(\overline{BC}\)[/tex]



Answer :

GinnyAnswer
To determine which side of the triangular rooftop terrace has the greatest length, we need to analyze the given angles of triangle [tex]$ABC$[/tex]:

- Measure of [tex]$\angle A = 55^{\circ}$[/tex]
- Measure of [tex]$\angle B = 65^{\circ}$[/tex]
- Measure of [tex]$\angle C = 60^{\circ}$[/tex]

First, recall a fundamental property of triangles: the side opposite the largest angle is the longest side. Let's identify the largest angle in triangle [tex]$ABC$[/tex].

- [tex]$\angle A$[/tex] measures [tex]$55^{\circ}$[/tex]
- [tex]$\angle B$[/tex] measures [tex]$65^{\circ}$[/tex]
- [tex]$\angle C$[/tex] measures [tex]$60^{\circ}$[/tex]

Among these angles, [tex]$\angle B = 65^{\circ}$[/tex] is the largest. Therefore, the side opposite [tex]$\angle B$[/tex] will have the greatest length. In triangle [tex]$ABC$[/tex], the side opposite [tex]$\angle B$[/tex] is side [tex]$\overline{AC}$[/tex].

Thus, the side of the terrace with the greatest length is [tex]$\overline{AC}$[/tex].

The correct answer is:
A. [tex]$\overline{AC}$[/tex]