https://file.aiquickdraw.com/mathbot/file/1727038129135b4g5zkpm.jpg

Let's analyze the problem from the image.

We are given a triangle \( ABC \) with the following information:
- \( C = 115^\circ \)
- \( a = 61 \)
- \( b = 15 \)

We are asked to solve the triangle, meaning we need to find:
1. \( A \) (the angle at vertex \( A \)),
2. \( B \) (the angle at vertex \( B \)),
3. \( c \) (the length of side \( c \)).

We can use the **Law of Sines** to find the missing angles and sides:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
We already know \( C \), so we can first find angle \( B \) using the Law of Sines, and then use the fact that the sum of angles in a triangle is \( 180^\circ \) to find \( A \).

### Step 1: Use the Law of Sines to find \( B \)

\[
\frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]

Let me compute \( B \).The calculations give us the following angles:
- \( B = 12.9^\circ \)
- \( A = 52.1^\circ \)

### Step 2: Use the Law of Sines to find side \( c \)

Now that we know angles \( A \) and \( B \), we can use the Law of Sines again to find \( c \). The formula is:

\[
\frac{a}{\sin(A)} = \frac{c}{\sin(C)}
\]

Let me calculate the length of side \( c \).

Consider a triangle ABC. Suppose that C = 115°, a = 61, and b = 15. Solve for the angles A, B, and the side c of the triangle.

Learn how to solve triangle ABC with angle C = 115°, side a = 61, and side b = 15. Using the Law of Sines and the Triangle Angle Sum Theorem, this step-by-step guide finds the unknown angles A, B, and side c.

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