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The problem you're working on involves solving a triangle using the **Law of Sines**. Here is a breakdown of the information provided:

Given:
- Angle \( A = 71^\circ \)
- Angle \( C = 26^\circ \)
- Side \( c = 46 \)

### Step-by-Step Solution:

1. **Find the remaining angle \( B \):**

   Since the sum of the interior angles in any triangle is always \( 180^\circ \), you can find angle \( B \) using the equation:
   \[
   B = 180^\circ - A - C = 180^\circ - 71^\circ - 26^\circ = 83^\circ
   \]

2. **Apply the Law of Sines:**
   
   The Law of Sines states:
   \[
   \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
   \]
   
   You can use this to find the unknown sides \( a \) and \( b \).

3. **Solve for side \( a \):**

   Using the Law of Sines for side \( a \):
   \[
   \frac{a}{\sin A} = \frac{c}{\sin C}
   \]
   Substituting the known values:
   \[
   \frac{a}{\sin 71^\circ} = \frac{46}{\sin 26^\circ}
   \]
   Solving for \( a \):
   \[
   a = \frac{46 \times \sin 71^\circ}{\sin 26^\circ}
   \]

4. **Solve for side \( b \):**

   Similarly, to find side \( b \):
   \[
   \frac{b}{\sin B} = \frac{c}{\sin C}
   \]
   Substituting the known values:
   \[
   \frac{b}{\sin 83^\circ} = \frac{46}{\sin 26^\circ}
   \]
   Solving for \( b \):
   \[
   b = \frac{46 \times \sin 83^\circ}{\sin 26^\circ}
   \]

I'll compute these values now.The solutions for the triangle are:

- \( a = 99.2 \)
- \( b = 104.2 \)
- \( B = 83^\circ \)

Let me know if you have any questions or need further clarification!

Here are 5 related questions to expand your understanding:
1. How is the Law of Sines applied to non-right triangles?
2. What is the relationship between the angles and sides of any triangle?
3. How would you solve the triangle if two sides and one angle were given instead?
4. How can the Law of Cosines be used in a similar scenario?
5. What is the difference between the Law of Sines and the Law of Cosines?

**Tip:** Always ensure your angles are in degrees (or radians) when using trigonometric functions in calculators!

Consider a triangle ABC with c = 46, A = 71°, and C = 26°. Solve the triangle using the Law of Sines.

Solve triangle ABC where A = 71°, C = 26°, and c = 46 using the Law of Sines. Learn how to calculate the unknown sides and angles step by step, suitable for students in Grades 9-11.

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