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The image displays a trigonometry problem involving solving a triangle using the Law of Sines. Given values are:

- \( b = 15 \)
- \( a = 59^\circ \)
- \( B = 76^\circ \)

We are asked to solve for angle \( A \), angle \( C \), and side \( c \).

### Step 1: Find Angle \( C \)
The sum of the angles in a triangle must be \( 180^\circ \), so we can calculate angle \( C \):

\[
C = 180^\circ - A - B
\]
Substituting the known value for \( B \):
\[
C = 180^\circ - 59^\circ - 76^\circ = 45^\circ
\]

### Step 2: Use the Law of Sines to Find Side \( c \)
The Law of Sines states:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
We can rearrange to find side \( c \):
\[
c = \frac{b \cdot \sin C}{\sin B}
\]
Substituting the known values for \( b = 15 \), \( C = 45^\circ \), and \( B = 76^\circ \):
\[
c = \frac{15 \cdot \sin 45^\circ}{\sin 76^\circ}
\]
Using sine values:
\[
c = \frac{15 \cdot 0.7071}{0.9703} \approx \frac{10.6065}{0.9703} \approx 10.93
\]

### Final Solution:
- \( A = 59^\circ \)
- \( C = 45^\circ \)
- \( c \approx 10.93 \)

Would you like more details or have any questions? 

Here are 5 related questions:
1. How is the Law of Sines used to solve non-right triangles?
2. Can the Law of Sines apply to any triangle?
3. How do we decide which law to use (Sines vs. Cosines) in a given triangle?
4. How do ambiguous cases arise in Law of Sines problems?
5. How can we apply the Law of Cosines if all sides are known but no angles?

**Tip:** Always double-check angle sums to ensure they add to 180°, ensuring accuracy in trigonometry problems!

Solve the triangle where b = 15, a = 59°, and B = 76° using the Law of Sines.

Solve a triangle using the Law of Sines with b = 15, a = 59°, and B = 76°. Learn to find the missing angles and side using key trigonometry concepts and formulas.

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