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
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![**Problem 10: Find \( m \angle A \)**
The diagram presents a triangle \(\triangle ABC\) with the following details:
- Side \( AC \) measures 32 miles.
- Side \( BC \) measures 29 miles.
- Angle \( \angle ABC \) is 98 degrees.
To find \( m \angle A \), we can use the Law of Sines or the Law of Cosines. Here, using the Law of Cosines is more straightforward due to the given angle and sides:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
Where:
- \( C \) is the angle at \( B \), which is 98 degrees.
- \( a = 29 \) miles, \( b = 32 \) miles, and \( c \) is opposite \( \angle A \).
After calculating using the cosine rule, you can find \( m \angle A \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F902e7e06-dd9d-47fe-961b-7a721406cdf1%2F60ab45dc-5917-4aa2-a0e6-2f4538a4c0a4%2F7optpxl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 10: Find \( m \angle A \)**
The diagram presents a triangle \(\triangle ABC\) with the following details:
- Side \( AC \) measures 32 miles.
- Side \( BC \) measures 29 miles.
- Angle \( \angle ABC \) is 98 degrees.
To find \( m \angle A \), we can use the Law of Sines or the Law of Cosines. Here, using the Law of Cosines is more straightforward due to the given angle and sides:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
Where:
- \( C \) is the angle at \( B \), which is 98 degrees.
- \( a = 29 \) miles, \( b = 32 \) miles, and \( c \) is opposite \( \angle A \).
After calculating using the cosine rule, you can find \( m \angle A \).
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