Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
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].
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.