Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
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].
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.