Use the Law of Sines to solve the triangle. Round your answers to two decimal places. A = 100°, a = 122, c = 14 C = B = b =
Use the Law of Sines to solve the triangle. Round your answers to two decimal places. A = 100°, a = 122, c = 14 C = B = 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°.
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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.
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![**Triangle Solution Using the Law of Sines**
**Problem Statement:**
Use the Law of Sines to solve the triangle. Round your answers to two decimal places.
\[ A = 100^\circ, \ a = 122, \ c = 14 \]
**To Find:**
\[ C = \,\,\,\,\,\,\,\,\,\,\,^\circ \]
\[ B = \,\,\,\,\,\,\,\,\,\,\,^\circ \]
\[ b = \,\,\,\,\,\,\,\,\,\,\, \]
**Explanation:**
The Law of Sines formula states that:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
Given:
\[ A = 100^\circ \]
\[ a = 122 \]
\[ c = 14 \]
**Step-by-Step Solution:**
1. **Calculate Angle \(C\):**
\[
\frac{122}{\sin(100^\circ)} = \frac{14}{\sin(C)}
\]
Solve for \(\sin(C)\):
\[
\sin(C) = \sin(100^\circ) \times \frac{14}{122}
\]
Find \(\sin(100^\circ)\) using a calculator and proceed with the division and multiplication.
2. **Calculate Angle \(B\):**
Since the sum of angles in a triangle is always \(180^\circ\):
\[
B = 180^\circ - A - C
\]
3. **Calculate Side \(b\):**
Using the previously calculated angles:
\[
\frac{b}{\sin(B)} = \frac{a}{\sin(A)}
\]
Solve for \(b\):
\[
b = \frac{122 \times \sin(B)}{\sin(100^\circ)}
\]
Note: Use a scientific calculator to compute sine values and verify your calculations. Write down your answer for \(C\), \(B\), and \(b\) rounded to two decimal places.
**Answer:**
\[ C = \,\,\,\,\,\,\,\,\,\,\,^\circ \]
\[ B = \,\,\,\,\,\,\,\,\,\,\,^\circ \]
\[ b = \,\,\,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06f55c03-0ff2-4f1b-a27d-6e1bf7c58dcc%2F6ed5f94b-36ca-46c8-af9a-163f1df73dea%2Fi1c93_processed.png&w=3840&q=75)
Transcribed Image Text:**Triangle Solution Using the Law of Sines**
**Problem Statement:**
Use the Law of Sines to solve the triangle. Round your answers to two decimal places.
\[ A = 100^\circ, \ a = 122, \ c = 14 \]
**To Find:**
\[ C = \,\,\,\,\,\,\,\,\,\,\,^\circ \]
\[ B = \,\,\,\,\,\,\,\,\,\,\,^\circ \]
\[ b = \,\,\,\,\,\,\,\,\,\,\, \]
**Explanation:**
The Law of Sines formula states that:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
Given:
\[ A = 100^\circ \]
\[ a = 122 \]
\[ c = 14 \]
**Step-by-Step Solution:**
1. **Calculate Angle \(C\):**
\[
\frac{122}{\sin(100^\circ)} = \frac{14}{\sin(C)}
\]
Solve for \(\sin(C)\):
\[
\sin(C) = \sin(100^\circ) \times \frac{14}{122}
\]
Find \(\sin(100^\circ)\) using a calculator and proceed with the division and multiplication.
2. **Calculate Angle \(B\):**
Since the sum of angles in a triangle is always \(180^\circ\):
\[
B = 180^\circ - A - C
\]
3. **Calculate Side \(b\):**
Using the previously calculated angles:
\[
\frac{b}{\sin(B)} = \frac{a}{\sin(A)}
\]
Solve for \(b\):
\[
b = \frac{122 \times \sin(B)}{\sin(100^\circ)}
\]
Note: Use a scientific calculator to compute sine values and verify your calculations. Write down your answer for \(C\), \(B\), and \(b\) rounded to two decimal places.
**Answer:**
\[ C = \,\,\,\,\,\,\,\,\,\,\,^\circ \]
\[ B = \,\,\,\,\,\,\,\,\,\,\,^\circ \]
\[ b = \,\,\,
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