Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer b A = 45°, a = 4.9, b = 13.1 B =
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer b A = 45°, a = 4.9, b = 13.1 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
Concept explainers
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
100%
Attached _10ASK.png
![### Topic: Solving Triangles Using the Law of Sines
#### Problem Statement:
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.)
Given:
\[
A = 45^\circ, \quad a = 4.9, \quad b = 13.1
\]
Find:
\[
B = \quad \boxed{\text{ }}^\circ
\]
\[
C = \quad \boxed{\text{ }}^\circ
\]
\[
c = \quad \boxed{\text{ }}
\]
**Note:** To solve the above triangle, apply the Law of Sines which states:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
### Explanation:
1. **Calculate Angle \( B \):**
Using the Law of Sines:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)}
\]
Substitute the known values:
\[
\frac{4.9}{\sin(45^\circ)} = \frac{13.1}{\sin(B)}
\]
Solve for \( \sin(B) \).
2. **Determine if there are two possible solutions for \( \sin(B) \).**
If \( \sin(B) \leq 1 \), analyze both possible angles \( B \) using \( B \) and \( 180^\circ - B \).
3. **Calculate Angle \( C \)**:
Using the angle sum property of a triangle:
\[
C = 180^\circ - A - B
\]
4. **Compute \( c \)** using the Law of Sines:
\[
\frac{a}{\sin(A)} = \frac{c}{\sin(C)}
\]
### Solution(s):
1. Calculate \( B \) and determine if the triangle is valid.
2. Calculate \( C \) based on the angle sum property.
3. Calculate the length \( c \).
**Submit your answers rounded to two decimal places in the provided boxes. If a triangle is not possible, enter "IMPOSSIBLE](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06f55c03-0ff2-4f1b-a27d-6e1bf7c58dcc%2Fb60cdf7f-9896-4c7f-98f0-125bb5c9900e%2Ficjfjm_processed.png&w=3840&q=75)
Transcribed Image Text:### Topic: Solving Triangles Using the Law of Sines
#### Problem Statement:
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.)
Given:
\[
A = 45^\circ, \quad a = 4.9, \quad b = 13.1
\]
Find:
\[
B = \quad \boxed{\text{ }}^\circ
\]
\[
C = \quad \boxed{\text{ }}^\circ
\]
\[
c = \quad \boxed{\text{ }}
\]
**Note:** To solve the above triangle, apply the Law of Sines which states:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
### Explanation:
1. **Calculate Angle \( B \):**
Using the Law of Sines:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)}
\]
Substitute the known values:
\[
\frac{4.9}{\sin(45^\circ)} = \frac{13.1}{\sin(B)}
\]
Solve for \( \sin(B) \).
2. **Determine if there are two possible solutions for \( \sin(B) \).**
If \( \sin(B) \leq 1 \), analyze both possible angles \( B \) using \( B \) and \( 180^\circ - B \).
3. **Calculate Angle \( C \)**:
Using the angle sum property of a triangle:
\[
C = 180^\circ - A - B
\]
4. **Compute \( c \)** using the Law of Sines:
\[
\frac{a}{\sin(A)} = \frac{c}{\sin(C)}
\]
### Solution(s):
1. Calculate \( B \) and determine if the triangle is valid.
2. Calculate \( C \) based on the angle sum property.
3. Calculate the length \( c \).
**Submit your answers rounded to two decimal places in the provided boxes. If a triangle is not possible, enter "IMPOSSIBLE
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 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