Use the Law of Cosines to determine the indicated angle 0. (Assume a = 22, 12, and c = 24. Round your answer to one decimal place.) b a
Use the Law of Cosines to determine the indicated angle 0. (Assume a = 22, 12, and c = 24. Round your answer to one decimal place.) b a
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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Question
![### Law of Cosines Problem
**Objective:**
Use the Law of Cosines to determine the indicated angle \( \theta \).
**Given:**
- Side \( a = 22 \)
- Side \( b = 12 \)
- Side \( c = 24 \)
**Instructions:**
Round your answer for angle \( \theta \) to one decimal place.
**Solution Approach:**
The Law of Cosines is used to find the angle \( \theta \) opposite side \( c \). The formula is:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(\theta)
\]
By rearranging the formula to solve for \( \cos(\theta) \), we have:
\[
\cos(\theta) = \frac{a^2 + b^2 - c^2}{2ab}
\]
Once \( \cos(\theta) \) is calculated, use the inverse cosine function to find \( \theta \).
**Diagram Explanation:**
The diagram is a triangle labeled with vertices \( A \), \( B \), and \( C \). The sides are labeled:
- \( a \) opposite vertex \( A \),
- \( b \) opposite vertex \( B \),
- \( c \) opposite vertex \( C \).
The angle \( \theta \) is between sides \( b \) and \( c \) at vertex \( A \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d0a7273-2200-4e06-b141-58f80df858e8%2Feea2795b-9a6f-46d8-b189-6a9d052dc66d%2Fhi6yweg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Law of Cosines Problem
**Objective:**
Use the Law of Cosines to determine the indicated angle \( \theta \).
**Given:**
- Side \( a = 22 \)
- Side \( b = 12 \)
- Side \( c = 24 \)
**Instructions:**
Round your answer for angle \( \theta \) to one decimal place.
**Solution Approach:**
The Law of Cosines is used to find the angle \( \theta \) opposite side \( c \). The formula is:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(\theta)
\]
By rearranging the formula to solve for \( \cos(\theta) \), we have:
\[
\cos(\theta) = \frac{a^2 + b^2 - c^2}{2ab}
\]
Once \( \cos(\theta) \) is calculated, use the inverse cosine function to find \( \theta \).
**Diagram Explanation:**
The diagram is a triangle labeled with vertices \( A \), \( B \), and \( C \). The sides are labeled:
- \( a \) opposite vertex \( A \),
- \( b \) opposite vertex \( B \),
- \( c \) opposite vertex \( C \).
The angle \( \theta \) is between sides \( b \) and \( c \) at vertex \( A \).
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