Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Question
thumb_up100%
Describe the methods, processes, and equations used to determine the missing side and angles.
attached image
![**Solve the following triangle:**
The diagram shows a triangle with the following information:
- One side is labeled as 2.3 cm.
- Another side is labeled as 1.1 cm.
- One angle is labeled as 105°.
**Task:**
Describe the methods, processes, and equations used to determine the missing side and angles.
**Explanation:**
1. **Triangle Description:** The given triangle has two known sides and one known angle, which is 105°. This is an oblique triangle (non-right triangle).
2. **Method to Solve:**
- **Law of Cosines:** Since two sides and the included angle are known, the Law of Cosines can be applied to find the third side. The formula is:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
where \( a \) and \( b \) are the known sides, \( C \) is the known angle (105°), and \( c \) is the unknown side.
- **Law of Sines:** Once the third side is found, the Law of Sines can be used to find the remaining angles. The formula is:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
where \( A \) and \( B \) are the unknown angles corresponding to the known and found sides.
3. **Process:**
- Use the Law of Cosines to calculate the length of the third side.
- Apply the Law of Sines to find one of the other angles.
- Calculate the remaining angle using the fact that the sum of angles in a triangle is 180°.
4. **Example Calculation:**
Start by calculating the third side using the Law of Cosines. Then use the Law of Sines to find another angle, remembering to adjust for angles that could be obtuse. Finally, find the last angle.
By following these steps, you will solve the triangle and determine all side lengths and angles.](https://content.bartleby.com/qna-images/question/692b4bb9-1b89-4fb4-be46-e3686210292a/875ad8ef-986a-409e-aaf5-254d7be8a8f5/za9lyp_processed.jpeg)
Transcribed Image Text:**Solve the following triangle:**
The diagram shows a triangle with the following information:
- One side is labeled as 2.3 cm.
- Another side is labeled as 1.1 cm.
- One angle is labeled as 105°.
**Task:**
Describe the methods, processes, and equations used to determine the missing side and angles.
**Explanation:**
1. **Triangle Description:** The given triangle has two known sides and one known angle, which is 105°. This is an oblique triangle (non-right triangle).
2. **Method to Solve:**
- **Law of Cosines:** Since two sides and the included angle are known, the Law of Cosines can be applied to find the third side. The formula is:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
where \( a \) and \( b \) are the known sides, \( C \) is the known angle (105°), and \( c \) is the unknown side.
- **Law of Sines:** Once the third side is found, the Law of Sines can be used to find the remaining angles. The formula is:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
where \( A \) and \( B \) are the unknown angles corresponding to the known and found sides.
3. **Process:**
- Use the Law of Cosines to calculate the length of the third side.
- Apply the Law of Sines to find one of the other angles.
- Calculate the remaining angle using the fact that the sum of angles in a triangle is 180°.
4. **Example Calculation:**
Start by calculating the third side using the Law of Cosines. Then use the Law of Sines to find another angle, remembering to adjust for angles that could be obtuse. Finally, find the last angle.
By following these steps, you will solve the triangle and determine all side lengths and angles.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps with 2 images
Knowledge Booster
Similar questions
- ® find Hhe equation$ the cirele paring Hhonyh 'the painta (-2,3 ), (-5, 6), and l2)arrow_forwardMake answer easy to readarrow_forwardAlice is flying a drone. The angle of depression from the drone to Alice is 35 degrees. The direct distance from Alice to the drone is 22.2 meters. What is the altitude of the drone? * 15.5 m 18.9 m 38.7 m O 12.7 marrow_forward
Recommended textbooks for you
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage Learning
Thomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON 
Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. Freeman
Calculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning