To solve this problem systematically, let’s follow these steps:

---

Step 1: Solve for the unknown angle using the angle sum formula

The angle sum formula for a triangle states:

$\text{Sum of angles in a triangle} = 180^\circ$

If two angles of the triangle are known, say $A$ and $B$, the third angle $C$ can be found as:

$C = 180^\circ - A - B$

---

Step 2: Apply the Law of Sines

The Law of Sines states:

$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$

Here:

• $a$, $b$, and $c$ are the lengths of the sides opposite to the angles $A$, $B$, and $C$, respectively.
• You will use this formula to find the side $AB$ based on the given information.

Rearrange for the unknown side:

To find the length $AB = c$, rearrange the Law of Sines:

$c = \frac{a \cdot \sin(C)}{\sin(A)}$

or equivalently:

$c = \frac{b \cdot \sin(C)}{\sin(B)}$

---

Step 3: Solve and Check

Let me know the numerical values of the given angles and sides, or upload an image if it’s available. With those details, I can compute the solution and verify calculations.

Would you like to proceed with this? If any of the values are unclear, feel free to share them now.

---

5 Related Questions:

1. Can you calculate all sides of the triangle using the Law of Sines?
2. What happens when two sides and one angle are given in a triangle?
3. How does the Law of Cosines differ from the Law of Sines?
4. Can the Law of Sines apply to non-obtuse triangles?
5. Why do we need trigonometric functions to solve triangles?

Tip:

Always ensure the angles are in the correct units (degrees or radians) based on your calculator's settings when solving trigonometric problems.