Explanation Given: The sides and the angle of the triangle are a = 5.240 , b = 4.446 and B = 48.13 ° . Formula used: If a, b and c are the lengths of the sides of the triangle and A, B and C are the three angles opposite to the sides of the triangle, then the law of sines is given by, a sin A = b sin B = c sin C . Procedure used: This is the case 2(Two sides and one angle) and so, the possibilities of the number of solutions are given by, No solution if b < a sin B . A right triangle solution if b = a sin B . Two solutions if a sin B < b < a . One solution if b > a . Calculation: The given values satisfy the condition (3). a sin B < b < a 5.240 sin 48.13 ° < 4.446 < 5.240 3.902 < 4.446 < 5.240 Thus, there would be two solutions. Use the law of sines to obtain the angle A . b sin B = a sin A 4.446 sin 48.13 ° = 5.240 sin A sin A = ( 5.240 ) ( sin 48.13 ° ) 4.446 sin A = ( 5.240 ) ( 0.744 ) 4.446 Solve ( 5.240 ) ( 0.744 ) 4.446 and take the sine inverse of it as follows. sin A = 3.898 4.446 A = sin − 1 ( 0.876 ) A = 61.36 ° The new angle A ′ in the second quadrant is given by, A ' = 180 ° − 61.36 ° A ' = 118.64 ° Find C and C ′ by use of the fact that sum of the interior angles of triangle is 180 ° . C = 180 ° − ( 61

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

See similar textbooks

Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Videos

Question

Chapter 9.5, Problem 15E

To determine

To solve: The triangle for the given values.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.5, Problem 14E

Chapter 9.5, Problem 16E

Students have asked these similar questions

Refer to page 10 for properties of Banach and Hilbert spaces. Instructions: 1. Analyze the normed vector space provided in the link and determine if it is complete. 2. Discuss the significance of inner products in Hilbert spaces. 3. Evaluate examples of Banach spaces that are not Hilbert spaces. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]

Refer to page 1 for eigenvalue decomposition techniques. Instructions: 1. Analyze the matrix provided in the link to calculate eigenvalues and eigenvectors. 2. Discuss how eigenvalues and eigenvectors are applied in solving systems of linear equations. 3. Evaluate the significance of diagonalizability in matrix transformations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]

Refer to page 4 for the definitions of sequence convergence. Instructions: 1. Analyze the sequence in the link and prove its convergence or divergence. 2. Discuss the difference between pointwise and uniform convergence for function sequences. 3. Evaluate real-world scenarios where uniform convergence is critical. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]

Chapter 9 Solutions

Basic Technical Mathematics

Ch. 9.1 - For the vectors in Example 2, show that R = B + C...Ch. 9.1 - Prob. 2PE Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.