Use the Law of Sines to solve the triangle. Round your answers to two decimal places. C = 94.70°, a = 35, c = 50 A = B = b =
Use the Law of Sines to solve the triangle. Round your answers to two decimal places. C = 94.70°, a = 35, c = 50 A = B = b =
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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![**Using the Law of Sines to Solve a Triangle**
In this educational example, we will solve the triangle using the Law of Sines. We will round our answers to two decimal places. Given data for the triangle are:
- Angle \( C = 94.70^\circ \)
- Side \( a = 35 \)
- Side \( c = 50 \)
To solve for the unknown values \( A \), \( B \), and \( b \):
- \( A \) is the measure of angle \( A \) (in degrees).
- \( B \) is the measure of angle \( B \) (in degrees).
- \( b \) is the length of side \( b \).
Here are the values to be determined:
- \( A = \) _______________ \( ^\circ \)
- \( B = \) _______________ \( ^\circ \)
- \( b = \) _______________
**Steps to Solve the Triangle:**
1. **Determine Angle \( A \) and \( B \):**
Since the sum of angles in a triangle is \( 180^\circ \),
\[
A + B + C = 180^\circ \implies A + B + 94.70^\circ = 180^\circ
\]
Let's denote \( A + B = 180^\circ - 94.70^\circ \).
2. **Use the Law of Sines** to solve for one of the unknown sides or angles:
The Law of Sines states:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Since we already know \( a \), \( c \), and \( C \), we can solve for one remaining angle and the side \( b \).
3. Solving for one of the angles (for demonstration, let's solve \( A \)):
\[
\frac{35}{\sin A} = \frac{50}{\sin 94.70^\circ}
\]
4. Once \( A \) is found, use it to find \( B \) as:
\[
B = 180^\circ - A - 94.70^\circ
\]
5. Finally, solve for side \( b \) using the Law of Sines after \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06f55c03-0ff2-4f1b-a27d-6e1bf7c58dcc%2F744b398f-79f8-4ef0-8144-53976f81cae0%2F7ovzn4o_processed.png&w=3840&q=75)
Transcribed Image Text:**Using the Law of Sines to Solve a Triangle**
In this educational example, we will solve the triangle using the Law of Sines. We will round our answers to two decimal places. Given data for the triangle are:
- Angle \( C = 94.70^\circ \)
- Side \( a = 35 \)
- Side \( c = 50 \)
To solve for the unknown values \( A \), \( B \), and \( b \):
- \( A \) is the measure of angle \( A \) (in degrees).
- \( B \) is the measure of angle \( B \) (in degrees).
- \( b \) is the length of side \( b \).
Here are the values to be determined:
- \( A = \) _______________ \( ^\circ \)
- \( B = \) _______________ \( ^\circ \)
- \( b = \) _______________
**Steps to Solve the Triangle:**
1. **Determine Angle \( A \) and \( B \):**
Since the sum of angles in a triangle is \( 180^\circ \),
\[
A + B + C = 180^\circ \implies A + B + 94.70^\circ = 180^\circ
\]
Let's denote \( A + B = 180^\circ - 94.70^\circ \).
2. **Use the Law of Sines** to solve for one of the unknown sides or angles:
The Law of Sines states:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Since we already know \( a \), \( c \), and \( C \), we can solve for one remaining angle and the side \( b \).
3. Solving for one of the angles (for demonstration, let's solve \( A \)):
\[
\frac{35}{\sin A} = \frac{50}{\sin 94.70^\circ}
\]
4. Once \( A \) is found, use it to find \( B \) as:
\[
B = 180^\circ - A - 94.70^\circ
\]
5. Finally, solve for side \( b \) using the Law of Sines after \(
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