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A building has a triangular rooftop terrace modeled by triangle [tex]\(ABC\)[/tex]. In triangle [tex]\(ABC\)[/tex]:

[tex]\(\angle A = 55^\circ\)[/tex]
[tex]\(\angle B = 65^\circ\)[/tex]
[tex]\(\angle C = 60^\circ\)[/tex]

Which side of the terrace has the greatest length?

A. [tex]\(\overline{AC}\)[/tex]
B. Cannot be determined
C. [tex]\(\overline{BC}\)[/tex]
D. [tex]\(\overline{AB}\)[/tex]



Answer :

GinnyAnswer
To determine which side of triangle [tex]\(ABC\)[/tex] has the greatest length, we need to consider the relationship between the angles and the sides of a triangle. In any triangle, the side opposite the largest angle is the longest side.

Let's examine the given angles:
- [tex]\(\angle A = 55^\circ\)[/tex]
- [tex]\(\angle B = 65^\circ\)[/tex]
- [tex]\(\angle C = 60^\circ\)[/tex]

First, we identify the largest angle among the given angles. Comparing the angles:
- [tex]\(55^\circ < 60^\circ < 65^\circ\)[/tex]

Thus, [tex]\(\angle B\)[/tex] is the largest angle at [tex]\(65^\circ\)[/tex].

According to triangle properties, the side opposite the largest angle is the longest side. In this triangle, the side opposite [tex]\(\angle B\)[/tex] is [tex]\(\overline{AC}\)[/tex].

Hence, the side [tex]\( \overline{AC} \)[/tex] has the greatest length.

So, the correct answer is:
A. [tex]\(\overline{AC}\)[/tex]

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