The Law of Sines is an important tool for figuring out oblique triangles. Oblique triangles are triangles that do not have a right angle.

The Law of Sines tells us that the ratio of a triangle's side lengths to the sine of their opposite angles is equal. Here's how it looks:

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

How to Use the Law of Sines:

1. Identify What You Know:

   • You might have two angles and one side (known as AAS or ASA).
   • Or you could have two sides and one angle that is not between them (called SSA).

2. Find Missing Angles:

   • Remember that the angles in a triangle add up to 180 degrees:
     $A + B + C = 180^\circ$.

3. Calculate Missing Sides:

   • You can rearrange the Law of Sines to find unknown sides:
     $a = \frac{b \cdot \sin A}{\sin B}$

Where is the Law of Sines Used?

• It’s helpful in fields like navigation and architecture, as well as in many problems involving triangle measurements.
• About 30% of geometry problems involve oblique triangles, which shows how important the Law of Sines is.