Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.) A = 120°, a = 124, b = 104 B = C = C =
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.) A = 120°, a = 124, b = 104 B = C = C =
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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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 a Triangle
**Problem Statement:**
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.)
**Given:**
- Angle \( A = 120^\circ \)
- Side \( a = 124 \)
- Side \( b = 104 \)
**Find:**
- Angle \( B \) = ______ \( \circ \)
- Angle \( C \) = ______ \( \circ \)
- Side \( c \) = ______
**Solution:**
1. **Apply the Law of Sines** \( \left( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \right) \).
2. **Solve for Angle \( B \):**
\[ \sin B = \frac{b \cdot \sin A}{a} \]
3. **Determine Angle \( C \):**
\[ C = 180^\circ - A - B \]
4. **Calculate Side \( c \) Using the Law of Sines:**
\[ \frac{c}{\sin C} = \frac{a}{\sin A} \]
\[ c = a \cdot \frac{\sin C}{\sin A} \]
If multiple solutions exist, consider:
- The Ambiguous Case for angle B, where there can be two possible values for \( B \) (one acute and one obtuse) leading to two different triangles.
**Insert your derived values for \( B \), \( C \), and \( c \) accordingly. If no valid triangle is possible due to computational or geometric contradictions, indicate 'IMPOSSIBLE' in each corresponding answer blank.**
**Note:**
Ensure you round your answers to two decimal places as per the instructions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fab864d-7419-4b8c-bc50-25971d273c3c%2Fc168b6fc-0e5e-4c52-a9d3-d0e001a26da9%2F8wbdsd4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Using the Law of Sines to Solve a Triangle
**Problem Statement:**
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.)
**Given:**
- Angle \( A = 120^\circ \)
- Side \( a = 124 \)
- Side \( b = 104 \)
**Find:**
- Angle \( B \) = ______ \( \circ \)
- Angle \( C \) = ______ \( \circ \)
- Side \( c \) = ______
**Solution:**
1. **Apply the Law of Sines** \( \left( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \right) \).
2. **Solve for Angle \( B \):**
\[ \sin B = \frac{b \cdot \sin A}{a} \]
3. **Determine Angle \( C \):**
\[ C = 180^\circ - A - B \]
4. **Calculate Side \( c \) Using the Law of Sines:**
\[ \frac{c}{\sin C} = \frac{a}{\sin A} \]
\[ c = a \cdot \frac{\sin C}{\sin A} \]
If multiple solutions exist, consider:
- The Ambiguous Case for angle B, where there can be two possible values for \( B \) (one acute and one obtuse) leading to two different triangles.
**Insert your derived values for \( B \), \( C \), and \( c \) accordingly. If no valid triangle is possible due to computational or geometric contradictions, indicate 'IMPOSSIBLE' in each corresponding answer blank.**
**Note:**
Ensure you round your answers to two decimal places as per the instructions.
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