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

Sagot :

GinnyAnswer
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]
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