Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To determine which side of a triangular rooftop terrace (modeled by triangle \(ABC\)) has the greatest length, we can use the properties of triangles and angle-side relationships. Specifically, we will utilize the Law of Sines and the property that in any triangle, the side opposite the largest angle is the longest.
In triangle \(ABC\):
- The measure of \(\angle A\) is \(55^\circ\).
- The measure of \(\angle B\) is \(65^\circ\).
- The measure of \(\angle C\) is \(60^\circ\).
Step-by-step, here is how we can determine which side is the longest:
1. Identify the Largest Angle:
We compare the given angle measures:
- \(\angle A = 55^\circ\)
- \(\angle B = 65^\circ\)
- \(\angle C = 60^\circ\)
Clearly, \(\angle B = 65^\circ\) is the largest angle among \(\angle A\), \(\angle B\), and \(\angle C\).
2. Determine the Side Opposite the Largest Angle:
In any triangle, the side opposite the largest angle is the longest. For our triangle \(ABC\):
- The side opposite \(\angle A\) (\(55^\circ\)) is \(\overline{BC}\).
- The side opposite \(\angle B\) (\(65^\circ\)) is \(\overline{AC}\).
- The side opposite \(\angle C\) (\(60^\circ\)) is \(\overline{AB}\).
Since \(\angle B\) (\(65^\circ\)) is the largest angle, the longest side is \(\overline{AC}\).
Thus, the correct answer is:
[tex]\[ \boxed{\overline{AC}} \][/tex]
So, the side of the terrace with the greatest length is \(\overline{AC}\). Therefore, the final answer is:
A. [tex]\(\overline{AC}\)[/tex].
In triangle \(ABC\):
- The measure of \(\angle A\) is \(55^\circ\).
- The measure of \(\angle B\) is \(65^\circ\).
- The measure of \(\angle C\) is \(60^\circ\).
Step-by-step, here is how we can determine which side is the longest:
1. Identify the Largest Angle:
We compare the given angle measures:
- \(\angle A = 55^\circ\)
- \(\angle B = 65^\circ\)
- \(\angle C = 60^\circ\)
Clearly, \(\angle B = 65^\circ\) is the largest angle among \(\angle A\), \(\angle B\), and \(\angle C\).
2. Determine the Side Opposite the Largest Angle:
In any triangle, the side opposite the largest angle is the longest. For our triangle \(ABC\):
- The side opposite \(\angle A\) (\(55^\circ\)) is \(\overline{BC}\).
- The side opposite \(\angle B\) (\(65^\circ\)) is \(\overline{AC}\).
- The side opposite \(\angle C\) (\(60^\circ\)) is \(\overline{AB}\).
Since \(\angle B\) (\(65^\circ\)) is the largest angle, the longest side is \(\overline{AC}\).
Thus, the correct answer is:
[tex]\[ \boxed{\overline{AC}} \][/tex]
So, the side of the terrace with the greatest length is \(\overline{AC}\). Therefore, the final answer is:
A. [tex]\(\overline{AC}\)[/tex].
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.