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
![The task is to solve for ∠A, ∠B, and x in the given right triangle.
### Diagram Description
1. **Triangle Labeling**:
- The triangle is labeled with vertices A and B.
- There is a right angle at vertex B.
2. **Side Lengths**:
- The length of the side opposite angle A and adjacent to angle B is 2.62 cm.
- The length of the side opposite angle B and adjacent to angle A is 4.32 cm.
- The hypotenuse, opposite the right angle, is labeled as x.
### Analytical Steps
1. **Applying the Pythagorean Theorem**:
Use the formula \( a^2 + b^2 = c^2 \) where \( c \) is the hypotenuse.
\[
(2.62)^2 + (4.32)^2 = x^2
\]
2. **Solving for x**:
Calculate the square of each side and solve for the hypotenuse.
3. **Trigonometric Ratios**:
- Use sine and cosine ratios to find ∠A and ∠B.
- \(\sin A = \frac{\text{opposite}}{\text{hypotenuse}} \)
- \(\cos A = \frac{\text{adjacent}}{\text{hypotenuse}} \)
4. **Calculating Angles**:
- Use inverse trigonometric functions to find the angles.
- \(\angle A = \arcsin(\frac{2.62}{x})\)
- \(\angle B = \arccos(\frac{2.62}{x})\)
After performing these calculations, you will have determined the measures of ∠A, ∠B, and the length of the hypotenuse, x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4275793-d0d9-4c18-8132-1bc68d69e927%2Fbf4f106b-baa6-4e41-9a50-b93a83fd75f1%2F5fmu8u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The task is to solve for ∠A, ∠B, and x in the given right triangle.
### Diagram Description
1. **Triangle Labeling**:
- The triangle is labeled with vertices A and B.
- There is a right angle at vertex B.
2. **Side Lengths**:
- The length of the side opposite angle A and adjacent to angle B is 2.62 cm.
- The length of the side opposite angle B and adjacent to angle A is 4.32 cm.
- The hypotenuse, opposite the right angle, is labeled as x.
### Analytical Steps
1. **Applying the Pythagorean Theorem**:
Use the formula \( a^2 + b^2 = c^2 \) where \( c \) is the hypotenuse.
\[
(2.62)^2 + (4.32)^2 = x^2
\]
2. **Solving for x**:
Calculate the square of each side and solve for the hypotenuse.
3. **Trigonometric Ratios**:
- Use sine and cosine ratios to find ∠A and ∠B.
- \(\sin A = \frac{\text{opposite}}{\text{hypotenuse}} \)
- \(\cos A = \frac{\text{adjacent}}{\text{hypotenuse}} \)
4. **Calculating Angles**:
- Use inverse trigonometric functions to find the angles.
- \(\angle A = \arcsin(\frac{2.62}{x})\)
- \(\angle B = \arccos(\frac{2.62}{x})\)
After performing these calculations, you will have determined the measures of ∠A, ∠B, and the length of the hypotenuse, x.
Expert Solution
Step 1: Given information
Step by step
Solved in 3 steps with 3 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