Answered

IDNLearn.com connects you with a community of knowledgeable individuals ready to help. Join our community to access reliable and comprehensive responses to your questions from experienced professionals.

Select the correct answer.

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]

Sagot :

GinnyAnsweridn
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]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.