10. Triangle ABC has side lengths a = 79.1, b 54.3, andc= 48.6. What is the measure of angle A? 37.2 100.3° 88.9° 42.5°
10. Triangle ABC has side lengths a = 79.1, b 54.3, andc= 48.6. What is the measure of angle A? 37.2 100.3° 88.9° 42.5°
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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![### Problem Statement
10. Triangle \(ABC\) has side lengths \(a = 79.1\), \(b = 54.3\), and \(c = 48.6\). What is the measure of angle \(A\)?
#### Options:
- 37.2°
- 100.3°
- 88.9°
- 42.5°
### Explanation:
To find the measure of angle \(A\) in triangle \(ABC\) with the given side lengths \(a\), \(b\), and \(c\), you can use the Law of Cosines, which is given by:
\[ \cos(A) = \frac{b^2 + c^2 - a^2}{2bc} \]
### Steps:
1. Plug in the given side lengths into the formula:
\[
\cos(A) = \frac{54.3^2 + 48.6^2 - 79.1^2}{2 \times 54.3 \times 48.6}
\]
2. Calculate the values inside the formula step by step:
- Compute \(54.3^2\)
- Compute \(48.6^2\)
- Compute \(79.1^2\)
- Add the values of \(54.3^2\) and \(48.6^2\)
- Subtract the value of \(79.1^2\) from the sum
- Compute the denominator \(2 \times 54.3 \times 48.6\)
- Divide the results of the numerator by the denominator
3. Find the arccosine (inverse cosine) of the result to get the measure of angle \(A\).
By going through these steps, you will find that the measure of angle \(A\) matches with one of the given options.
### Graphs or Diagrams
There are no graphs or diagrams present in the problem statement to explain in detail.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c6fb9d5-7a44-4ded-b479-beba3f568d74%2F65848ed2-936a-40ef-b68a-dc7c6eeb8c69%2Fjgl7t9r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
10. Triangle \(ABC\) has side lengths \(a = 79.1\), \(b = 54.3\), and \(c = 48.6\). What is the measure of angle \(A\)?
#### Options:
- 37.2°
- 100.3°
- 88.9°
- 42.5°
### Explanation:
To find the measure of angle \(A\) in triangle \(ABC\) with the given side lengths \(a\), \(b\), and \(c\), you can use the Law of Cosines, which is given by:
\[ \cos(A) = \frac{b^2 + c^2 - a^2}{2bc} \]
### Steps:
1. Plug in the given side lengths into the formula:
\[
\cos(A) = \frac{54.3^2 + 48.6^2 - 79.1^2}{2 \times 54.3 \times 48.6}
\]
2. Calculate the values inside the formula step by step:
- Compute \(54.3^2\)
- Compute \(48.6^2\)
- Compute \(79.1^2\)
- Add the values of \(54.3^2\) and \(48.6^2\)
- Subtract the value of \(79.1^2\) from the sum
- Compute the denominator \(2 \times 54.3 \times 48.6\)
- Divide the results of the numerator by the denominator
3. Find the arccosine (inverse cosine) of the result to get the measure of angle \(A\).
By going through these steps, you will find that the measure of angle \(A\) matches with one of the given options.
### Graphs or Diagrams
There are no graphs or diagrams present in the problem statement to explain in detail.
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