25) To find the missing angle below, would you use the Law of Sines or Law of Cosines. Find the missing angle. 7 in. 10 in. с B C. Law of Sines,
25) To find the missing angle below, would you use the Law of Sines or Law of Cosines. Find the missing angle. 7 in. 10 in. с B C. Law of Sines,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Mathematics: Introduction to the Law of Sines and Law of Cosines
**Example Problem:**
To find the missing angle below, would you use the Law of Sines or Law of Cosines? Find the missing angle.
#### Triangle ABC
- **Angle A** = 112°
- **Side a (opposite to angle A)** = 7 in
- **Side c (opposite to angle C)** = 10 in
#### Provided Options:
A. Law of Cosines, ∠B = 43.5°
B. Law of Sines, ∠B = 40.5°
C. Law of Sines, ∠B = 60.5°
D. Law of Cosines, ∠B = 45.5°
The diagrams shows a triangle with vertices labeled A, B, and C. Angle A is marked as 112 degrees, side opposite to A (side BC) is 7 inches, and another side opposite to some angle is 10 inches.
Among the given options, choice B is marked as correct. Therefore, the missing angle B = 40.5° can be found using the Law of Sines.
**Detailed Explanation:**
The Law of Sines and Law of Cosines are two important tools in trigonometry for solving triangles, especially non-right triangles.
- **Law of Sines**: Used when we know either two angles and one side or two sides and a non-included angle.
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
- **Law of Cosines**: Used when we know either three sides or two sides and the included angle.
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
In this problem, we are given two sides and a non-included angle, which suggests using the Law of Sines.
- **Given**: Angle A = 112°, side opposite to A (a) = 7 in, side opposite to C (c) = 10 in.
- **Required**: Angle B.
Using the Law of Sines:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)}
\]
Substituting the given values:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5a061b4-0108-4a51-81fc-44207999c893%2F7d8a7fb0-4c05-4dfa-a528-36e5a28a2b00%2Fxz5p2er_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Mathematics: Introduction to the Law of Sines and Law of Cosines
**Example Problem:**
To find the missing angle below, would you use the Law of Sines or Law of Cosines? Find the missing angle.
#### Triangle ABC
- **Angle A** = 112°
- **Side a (opposite to angle A)** = 7 in
- **Side c (opposite to angle C)** = 10 in
#### Provided Options:
A. Law of Cosines, ∠B = 43.5°
B. Law of Sines, ∠B = 40.5°
C. Law of Sines, ∠B = 60.5°
D. Law of Cosines, ∠B = 45.5°
The diagrams shows a triangle with vertices labeled A, B, and C. Angle A is marked as 112 degrees, side opposite to A (side BC) is 7 inches, and another side opposite to some angle is 10 inches.
Among the given options, choice B is marked as correct. Therefore, the missing angle B = 40.5° can be found using the Law of Sines.
**Detailed Explanation:**
The Law of Sines and Law of Cosines are two important tools in trigonometry for solving triangles, especially non-right triangles.
- **Law of Sines**: Used when we know either two angles and one side or two sides and a non-included angle.
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
- **Law of Cosines**: Used when we know either three sides or two sides and the included angle.
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
In this problem, we are given two sides and a non-included angle, which suggests using the Law of Sines.
- **Given**: Angle A = 112°, side opposite to A (a) = 7 in, side opposite to C (c) = 10 in.
- **Required**: Angle B.
Using the Law of Sines:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)}
\]
Substituting the given values:
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