Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Using the Law of Cosines to Solve Oblique Triangles
#### Problem Statement:
**The following oblique triangle can be solved by using the Law of Cosines (SSS).**
The triangle ABC is given. The lengths of sides are:
- AB = 8 ft
- AC = 7 ft
- BC = a ft
#### Question:
**Can the following oblique triangle be solved by using the Law of Cosines (SSS)?**
- [ ] True
- [ ] False
#### Explanation:
The provided diagram illustrates an oblique triangle (a triangle that does not contain a right angle) with labeled vertices A, B, and C. The lengths of sides AB and AC are given as 8 feet and 7 feet, respectively. The side BC is labeled as \( a \).
#### Understanding the Concept:
The Law of Cosines is used to relate the lengths of the sides of a triangle to the cosine of one of its angles. It is particularly useful in solving oblique triangles in the following scenarios:
- Side-Side-Side (SSS): When all three sides of the triangle are known.
- Side-Angle-Side (SAS): When two sides and the included angle are known.
In this question, since the lengths of all three sides of the triangle are known, we can determine whether the Law of Cosines can be applied to solve for the unknown angles or other missing measurements.
**The Law of Cosines Formula:**
\[ c^2 = a^2 + b^2 - 2ab \cos(C) \]
Where:
- \( a \), \( b \), and \( c \) are the lengths of the sides,
- \( C \) is the angle opposite the side \( c \).
Using this formula, we can solve for any unknown angle when the lengths of all three sides are given, thus confirming if the statement provided is true or false.
**Answer Choices:**
- **True:** Select if the triangle can indeed be solved using the Law of Cosines with the given information.
- **False:** Select if the Law of Cosines is not applicable or if the given information is insufficient for solving the triangle.
#### Additional Information:
The interface provides two radio buttons to select the answer—'True' or 'False'. To navigate or submit the response, a left-arrow button is available. The display also includes status information regarding weather (87°F, Partly sunny)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febfa71ca-f003-4e76-b16d-d56ed3281ebe%2F6df9aa07-9d01-4a3c-bb17-7c9d1752a362%2F9hdjmd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Using the Law of Cosines to Solve Oblique Triangles
#### Problem Statement:
**The following oblique triangle can be solved by using the Law of Cosines (SSS).**
The triangle ABC is given. The lengths of sides are:
- AB = 8 ft
- AC = 7 ft
- BC = a ft
#### Question:
**Can the following oblique triangle be solved by using the Law of Cosines (SSS)?**
- [ ] True
- [ ] False
#### Explanation:
The provided diagram illustrates an oblique triangle (a triangle that does not contain a right angle) with labeled vertices A, B, and C. The lengths of sides AB and AC are given as 8 feet and 7 feet, respectively. The side BC is labeled as \( a \).
#### Understanding the Concept:
The Law of Cosines is used to relate the lengths of the sides of a triangle to the cosine of one of its angles. It is particularly useful in solving oblique triangles in the following scenarios:
- Side-Side-Side (SSS): When all three sides of the triangle are known.
- Side-Angle-Side (SAS): When two sides and the included angle are known.
In this question, since the lengths of all three sides of the triangle are known, we can determine whether the Law of Cosines can be applied to solve for the unknown angles or other missing measurements.
**The Law of Cosines Formula:**
\[ c^2 = a^2 + b^2 - 2ab \cos(C) \]
Where:
- \( a \), \( b \), and \( c \) are the lengths of the sides,
- \( C \) is the angle opposite the side \( c \).
Using this formula, we can solve for any unknown angle when the lengths of all three sides are given, thus confirming if the statement provided is true or false.
**Answer Choices:**
- **True:** Select if the triangle can indeed be solved using the Law of Cosines with the given information.
- **False:** Select if the Law of Cosines is not applicable or if the given information is insufficient for solving the triangle.
#### Additional Information:
The interface provides two radio buttons to select the answer—'True' or 'False'. To navigate or submit the response, a left-arrow button is available. The display also includes status information regarding weather (87°F, Partly sunny)
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