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...
Related questions
Question
![**Problem Statement:**
Given the triangle with sides of lengths 26 and 28, and an included angle of 42°, find the length of side \( x \) using the Law of Cosines. Round your final answer to 4 decimal places.
**Visualization:**
A triangle is depicted with:
- One side labeled 26
- Another side labeled 28
- The included angle between these two sides labeled 42°
- The side opposite the 42° angle labeled \( x \)
**Formula:**
To find the length of side \( x \), use the Law of Cosines:
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
where:
- \( a \) and \( b \) are the lengths of the known sides (26 and 28 respectively),
- \( C \) is the included angle (42°),
- \( c \) is the length of the side opposite the angle \( C \) (which we are solving for, labeled \( x \)).
**Solution:**
Using the formula:
\[ x^2 = 26^2 + 28^2 - 2 \cdot 26 \cdot 28 \cdot \cos(42^\circ) \]
Now solve for \( x \):
\[ x = \sqrt{26^2 + 28^2 - 2 \cdot 26 \cdot 28 \cdot \cos(42^\circ)} \]
You can plug in the values and use a calculator to obtain the numerical value. Finally, round the result to four decimal places.
**Answer:**
\[ x = \_\_\_\_ \] (This is for the student to fill in after calculation)
Note: Use a scientific calculator or an online computational tool to accurately compute the value and then round to four decimal places as requested.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc94e4e1c-3d4e-4486-b985-b30353acec86%2F573f7dfa-d968-4d35-8b7a-400ac2f335d8%2Fjjy6raa_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given the triangle with sides of lengths 26 and 28, and an included angle of 42°, find the length of side \( x \) using the Law of Cosines. Round your final answer to 4 decimal places.
**Visualization:**
A triangle is depicted with:
- One side labeled 26
- Another side labeled 28
- The included angle between these two sides labeled 42°
- The side opposite the 42° angle labeled \( x \)
**Formula:**
To find the length of side \( x \), use the Law of Cosines:
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
where:
- \( a \) and \( b \) are the lengths of the known sides (26 and 28 respectively),
- \( C \) is the included angle (42°),
- \( c \) is the length of the side opposite the angle \( C \) (which we are solving for, labeled \( x \)).
**Solution:**
Using the formula:
\[ x^2 = 26^2 + 28^2 - 2 \cdot 26 \cdot 28 \cdot \cos(42^\circ) \]
Now solve for \( x \):
\[ x = \sqrt{26^2 + 28^2 - 2 \cdot 26 \cdot 28 \cdot \cos(42^\circ)} \]
You can plug in the values and use a calculator to obtain the numerical value. Finally, round the result to four decimal places.
**Answer:**
\[ x = \_\_\_\_ \] (This is for the student to fill in after calculation)
Note: Use a scientific calculator or an online computational tool to accurately compute the value and then round to four decimal places as requested.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
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:
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