Law of Sines

📊 intermediate

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

Relates the lengths of the sides of any triangle to the sines of its angles.

Variables & Units

$a, b, c$

Lengths of triangle sides

Unit: Length units

$A, B, C$

Opposite angles

Unit: Degrees/Radians

Key Information

📐 Derived From

Area of a triangle expressed using sine functions.

💡 Example

Solving for a side when two angles and one side are known.

🔧 Applications

Surveying and navigation.

⚠️ Constraints

Ambiguous case (SSA) can lead to two possible solutions.

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