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

Which side of the terrace has the greatest length?

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

Sagot :

GinnyAnsweridn
To determine which side of the triangle has the greatest length, we need to refer to the properties of triangles and their angles. In any triangle, the side opposite the largest angle is the longest.

Given the triangle [tex]\( ABC \)[/tex] with the provided angle measures:
- [tex]\( \angle A = 55^\circ \)[/tex]
- [tex]\( \angle B = 65^\circ \)[/tex]
- [tex]\( \angle C = 60^\circ \)[/tex]

We observe that [tex]\( \angle B \)[/tex] is the largest angle in this triangle since:
[tex]\[ 65^\circ > 60^\circ > 55^\circ \][/tex]

According to the property mentioned, the side opposite to the largest angle in a triangle will have the greatest length. Therefore, the side opposite [tex]\( \angle B \)[/tex], which is side [tex]\( \overline{AC} \)[/tex], is the longest.

Thus, the side of the terrace with the greatest length is:

B. [tex]\( \overline{AC} \)[/tex]
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