To solve the triangle $\triangle ABC$ using the Law of Sines, follow these steps:

Given:

• $b = 46$
• $a = 60$
• $B = 112^\circ$

We need to find:

1. $C$ (angle)
2. $c$ (side)
3. $A$ (angle)

Step 1: Find angle $A$

Using the angle sum property of a triangle: $A + B + C = 180^\circ$ $A = 180^\circ - B - C = 180^\circ - 112^\circ - C$ We will calculate $A$ after finding $C$.

Step 2: Use the Law of Sines to find $C$

The Law of Sines states: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ Using $\frac{b}{\sin B} = \frac{c}{\sin C}$: $c = b \cdot \frac{\sin C}{\sin B}$ We’ll calculate $\sin B$ and other values once we know $C$.

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