Explanation Formula used: For any triangle with sides a, b and c , opposite angles A , B and C respectively, the law of Cosines and law of Sines can be defined as follows. Law of cosines: a 2 = b 2 + c 2 − 2 b c cos A This can be also written as follows. b 2 = a 2 + c 2 − 2 a c cos B c 2 = a 2 + b 2 − 2 a b cos C Law of sines: a sin A = b sin B = c sin C Calculation: Given that, the magnitude of A = 43.12 ° , a = 7.893 and b = 4.113 . Sketch the graph of the triangle with known measures as shown below in Figure 1. From Figure 1, it is observed that the two sides and the opposite angle of larger side of the triangle are known. Therefore, there will be unique solution for this triangle. Now, use the law of sines and find the B . a sin A = b sin B 7.893 sin 43.12 ° = 4.113 sin B sin B = 4

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

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, Problem 36RE

To determine

To solve: The triangle if A=43.12°,a=7.893 and b=4.113.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 35RE

Chapter 9, Problem 37RE

Students have asked these similar questions

6. [10 marks] Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of T. (a) How many vertices does BL(T) have? (b) How many edges does BL(T) have? Prove that your answers are correct.

4. [10 marks] Find both a matching of maximum size and a vertex cover of minimum size in the following bipartite graph. Prove that your answer is correct. ย ພ

5. [10 marks] Let G = (V,E) be a graph, and let X C V be a set of vertices. Prove that if |S||N(S)\X for every SCX, then G contains a matching M that matches every vertex of X (i.e., such that every x X is an end of an edge in M).

Chapter 9 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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.

The triangle if A = 43.12 ° , a = 7.893 and b = 4.113 .

Concept explainers

Videos

To solve: The triangle if A=43.12°,a=7.893 and b=4.113.

Want to see the full answer?

Chapter 9 Solutions