Answered

Find accurate and reliable answers to your questions on IDNLearn.com. Ask your questions and receive detailed and reliable answers from our experienced and knowledgeable community members.

Select the correct answer.

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]

Sagot :

GinnyAnsweridn
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]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.