Use the Law of Sines to solve the following triangle for c. Approximate your answers to the nearest tenths. b = 13.1 km, B = 12.7°, C= 100.0% 3 O 58.7 km 55.0 km 5.6 km 2.9 km
Use the Law of Sines to solve the following triangle for c. Approximate your answers to the nearest tenths. b = 13.1 km, B = 12.7°, C= 100.0% 3 O 58.7 km 55.0 km 5.6 km 2.9 km
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Using the Law of Sines in a Triangle**
### Objective:
Use the Law of Sines to solve the following triangle for side \( c \). Approximate your answers to the nearest tenths.
### Given Data:
- \( b = 13.1 \) km
- \( B = 12.7^\circ \)
- \( C = 100.0^\circ \)
### Problem:
Select the correct value for side \( c \).
### Options:
- \( 58.7 \) km
- \( 55.0 \) km
- \( 5.6 \) km
- \( 2.9 \) km
### Explanation of the Law of Sines:
The Law of Sines states:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
Where:
- \( a, b, \) and \( c \) are the sides of the triangle.
- \( A, B, \) and \( C \) are the angles opposite to these sides, respectively.
### Solution Plan:
1. **Calculate the value of \( \sin(B) \) and \( \sin(C) \)** using a calculator.
2. **Use the Law of Sines** to find side \( c \).
**Step-by-Step Calculation:**
\[
\frac{c}{\sin(C)} = \frac{b}{\sin(B)}
\]
Solve for \( c \):
\[
c = \frac{b \cdot \sin(C)}{\sin(B)}
\]
Insert the given values and compute the result.
### Conclusion:
After calculating, select the correct approximate value for \( c \) from the provided options. Ensure that the answer is rounded to the nearest tenth.
### Example Calculation:
For students to practice, they can substitute the known values into the formula and solve step-by-step using a scientific calculator.
This problem illustrates the practical application of the Law of Sines in solving triangles, which is fundamental in trigonometry.
---
**Note:**
Detailed step-by-step calculations and a tutorial video can be provided in the supplementary materials section for further learning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febfa71ca-f003-4e76-b16d-d56ed3281ebe%2Fcf5fca77-3926-4e59-bf0d-0186a6a149af%2Fcy2vo4c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using the Law of Sines in a Triangle**
### Objective:
Use the Law of Sines to solve the following triangle for side \( c \). Approximate your answers to the nearest tenths.
### Given Data:
- \( b = 13.1 \) km
- \( B = 12.7^\circ \)
- \( C = 100.0^\circ \)
### Problem:
Select the correct value for side \( c \).
### Options:
- \( 58.7 \) km
- \( 55.0 \) km
- \( 5.6 \) km
- \( 2.9 \) km
### Explanation of the Law of Sines:
The Law of Sines states:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
Where:
- \( a, b, \) and \( c \) are the sides of the triangle.
- \( A, B, \) and \( C \) are the angles opposite to these sides, respectively.
### Solution Plan:
1. **Calculate the value of \( \sin(B) \) and \( \sin(C) \)** using a calculator.
2. **Use the Law of Sines** to find side \( c \).
**Step-by-Step Calculation:**
\[
\frac{c}{\sin(C)} = \frac{b}{\sin(B)}
\]
Solve for \( c \):
\[
c = \frac{b \cdot \sin(C)}{\sin(B)}
\]
Insert the given values and compute the result.
### Conclusion:
After calculating, select the correct approximate value for \( c \) from the provided options. Ensure that the answer is rounded to the nearest tenth.
### Example Calculation:
For students to practice, they can substitute the known values into the formula and solve step-by-step using a scientific calculator.
This problem illustrates the practical application of the Law of Sines in solving triangles, which is fundamental in trigonometry.
---
**Note:**
Detailed step-by-step calculations and a tutorial video can be provided in the supplementary materials section for further learning.
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