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Sagot :
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]
- 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]
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