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]

Question

13-06-2024
Mathematics

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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 :

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GinnyAnsweridn GinnyAnsweridn · Answer 1 · 2024-06-13T10:51:34-04:00

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]

Sagot :

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