Use the Law of Sines to solve the following triangle for c. Approximate your answers to the nearest tenths. a = 92 cm, B = 43°, C = 36⁰. 12.3 cm 43.8 cm 63.9 cm 55.1 cm [
Use the Law of Sines to solve the following triangle for c. Approximate your answers to the nearest tenths. a = 92 cm, B = 43°, C = 36⁰. 12.3 cm 43.8 cm 63.9 cm 55.1 cm [
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Using the Law of Sines to Solve Triangles**
To solve the given triangle for side \( c \), we use the Law of Sines. The problem provides the following measurements:
- \( a = 92 \text{ cm} \)
- \( B = 43^\circ \)
- \( C = 36^\circ \)
### Question:
Use the Law of Sines to solve the following triangle for \( c \). Approximate your answers to the nearest tenths.
- 12.3 cm
- 43.8 cm
- 63.9 cm
- 55.1 cm
### Explanation:
The Law of Sines states:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
Given \( a \), \( B \), and \( C \), we need to find side \( c \).
To find angle \( A \), use the fact that the sum of the angles in any triangle is \( 180^\circ \):
\[ A = 180^\circ - B - C
= 180^\circ - 43^\circ - 36^\circ
= 101^\circ \]
Now, apply the Law of Sines:
\[ \frac{92}{\sin 101^\circ} = \frac{c}{\sin 36^\circ} \]
\[ c = \frac{92 \times \sin 36^\circ}{\sin 101^\circ} \]
Using a calculator, we find:
\[ \sin 101^\circ \approx 0.985 \]
\[ \sin 36^\circ \approx 0.588 \]
\[ c = \frac{92 \times 0.588}{0.985} \approx \frac{54.096}{0.985} \approx 54.9 \text{ cm} \]
So, the closest approximation to the calculated length of side \( c \) is 55.1 cm. However, since 54.9 is closer approximation, we may need to check if it aligns correctly with available options or unintended rounding errors.
The correct answer among the listed options is:
**55.1 cm**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc7859e1-a84c-4143-bc4d-4794151a052e%2F8165f5d3-d620-4344-a5db-7f65462e3aba%2Fvub46i3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using the Law of Sines to Solve Triangles**
To solve the given triangle for side \( c \), we use the Law of Sines. The problem provides the following measurements:
- \( a = 92 \text{ cm} \)
- \( B = 43^\circ \)
- \( C = 36^\circ \)
### Question:
Use the Law of Sines to solve the following triangle for \( c \). Approximate your answers to the nearest tenths.
- 12.3 cm
- 43.8 cm
- 63.9 cm
- 55.1 cm
### Explanation:
The Law of Sines states:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
Given \( a \), \( B \), and \( C \), we need to find side \( c \).
To find angle \( A \), use the fact that the sum of the angles in any triangle is \( 180^\circ \):
\[ A = 180^\circ - B - C
= 180^\circ - 43^\circ - 36^\circ
= 101^\circ \]
Now, apply the Law of Sines:
\[ \frac{92}{\sin 101^\circ} = \frac{c}{\sin 36^\circ} \]
\[ c = \frac{92 \times \sin 36^\circ}{\sin 101^\circ} \]
Using a calculator, we find:
\[ \sin 101^\circ \approx 0.985 \]
\[ \sin 36^\circ \approx 0.588 \]
\[ c = \frac{92 \times 0.588}{0.985} \approx \frac{54.096}{0.985} \approx 54.9 \text{ cm} \]
So, the closest approximation to the calculated length of side \( c \) is 55.1 cm. However, since 54.9 is closer approximation, we may need to check if it aligns correctly with available options or unintended rounding errors.
The correct answer among the listed options is:
**55.1 cm**
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