Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Example Problem 3: Triangle with Side Lengths**
In this example problem, we are presented with a triangle labeled \( \triangle MNP \). The vertices of the triangle are marked as \( M \), \( N \), and \( P \).
**Side Lengths:**
- The side \( MN \) has a length of 5.6 units.
- The side \( MP \) has a length of 5.3 units.
- The side \( NP \) has a length of 3.4 units.
To solve triangle-based problems, such as finding the angles using the side lengths, you can apply various rules and formulas, such as:
1. **The Law of Cosines:**
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
where \( a \), \( b \), and \( c \) are the side lengths, and \( C \) is the angle opposite side \( c \).
2. **The Law of Sines:**
\[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \]
where \( a \), \( b \), and \( c \) are the side lengths relative to angles \( A \), \( B \), and \( C \) respectively.
Understanding these fundamentals helps in solving various aspects of triangles, including determining unknown sides and angles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e82bb83-97a5-4174-a76b-39181a086848%2Fdf24aabc-931c-4395-925d-48660bf791c1%2Fzd28ekq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Problem 3: Triangle with Side Lengths**
In this example problem, we are presented with a triangle labeled \( \triangle MNP \). The vertices of the triangle are marked as \( M \), \( N \), and \( P \).
**Side Lengths:**
- The side \( MN \) has a length of 5.6 units.
- The side \( MP \) has a length of 5.3 units.
- The side \( NP \) has a length of 3.4 units.
To solve triangle-based problems, such as finding the angles using the side lengths, you can apply various rules and formulas, such as:
1. **The Law of Cosines:**
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
where \( a \), \( b \), and \( c \) are the side lengths, and \( C \) is the angle opposite side \( c \).
2. **The Law of Sines:**
\[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \]
where \( a \), \( b \), and \( c \) are the side lengths relative to angles \( A \), \( B \), and \( C \) respectively.
Understanding these fundamentals helps in solving various aspects of triangles, including determining unknown sides and angles.
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