Consider the triangle shown in the diagram below. В ZB а ZA A 07 C Suppose that mA = 85°, a = 6.31, and b = 4.24. (The diagram above is not necessarily to scale. a. What is the value of m/B?
Consider the triangle shown in the diagram below. В ZB а ZA A 07 C Suppose that mA = 85°, a = 6.31, and b = 4.24. (The diagram above is not necessarily to scale. a. What is the value of m/B?
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
 *(Note: replace image-link with the actual image link on the website)*
In the diagram, triangle \(ABC\) is labeled with angles and side lengths as follows:
- \( \angle A \) at vertex \( A \)
- \( \angle B \) at vertex \( B \)
- \( \angle C \) at vertex \( C \)
- Side \( a \) opposite \( \angle A \)
- Side \( b \) opposite \( \angle B \)
- Side \( c \) opposite \( \angle C \)
Given data:
- \( m \angle A = 85^\circ \)
- \( a = 6.31 \)
- \( b = 4.24 \)
The goal is to find:
a. The measure of \( m \angle B \)
b. The length of side \( c \)
### Steps to Solve
#### a. Finding \( m \angle B \)
Using the fact that the sum of angles in any triangle is \( 180^\circ \):
\[ m \angle A + m \angle B + m \angle C = 180^\circ \]
\[ 85^\circ + m \angle B + m \angle C = 180^\circ \]
To find \( m \angle B \), we first need \( m \angle C \), which can be determined using the Law of Sines once another angle and its opposite side are known.
#### b. Finding the length of side \( c \)
We'll use the Law of Sines:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
\[ \frac{6.31}{\sin 85^\circ} = \frac{4.24}{\sin B} = \frac{c}{\sin(180^\circ - 85^\circ - B)} \]
The students can use a calculator to input the values and solve the equations accurately.
### Interactive Section
Students are invited to enter their answer:
1. Angle \( m \angle B \):
\[ m \angle B = \boxed{ \, }^\circ \]
\[ \text{Preview} \]
2. Side length \( c \):
\[ c = \boxed{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F370a7c6f-923c-4e3e-b2e2-de29038e74c7%2Fb43123ab-114b-4154-afaa-187ba4281145%2Fc3n9lq_processed.png&w=3840&q=75)
Transcribed Image Text:### Analyzing a Triangle Using the Law of Sines
Consider the triangle shown in the diagram below:
 *(Note: replace image-link with the actual image link on the website)*
In the diagram, triangle \(ABC\) is labeled with angles and side lengths as follows:
- \( \angle A \) at vertex \( A \)
- \( \angle B \) at vertex \( B \)
- \( \angle C \) at vertex \( C \)
- Side \( a \) opposite \( \angle A \)
- Side \( b \) opposite \( \angle B \)
- Side \( c \) opposite \( \angle C \)
Given data:
- \( m \angle A = 85^\circ \)
- \( a = 6.31 \)
- \( b = 4.24 \)
The goal is to find:
a. The measure of \( m \angle B \)
b. The length of side \( c \)
### Steps to Solve
#### a. Finding \( m \angle B \)
Using the fact that the sum of angles in any triangle is \( 180^\circ \):
\[ m \angle A + m \angle B + m \angle C = 180^\circ \]
\[ 85^\circ + m \angle B + m \angle C = 180^\circ \]
To find \( m \angle B \), we first need \( m \angle C \), which can be determined using the Law of Sines once another angle and its opposite side are known.
#### b. Finding the length of side \( c \)
We'll use the Law of Sines:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
\[ \frac{6.31}{\sin 85^\circ} = \frac{4.24}{\sin B} = \frac{c}{\sin(180^\circ - 85^\circ - B)} \]
The students can use a calculator to input the values and solve the equations accurately.
### Interactive Section
Students are invited to enter their answer:
1. Angle \( m \angle B \):
\[ m \angle B = \boxed{ \, }^\circ \]
\[ \text{Preview} \]
2. Side length \( c \):
\[ c = \boxed{
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning