1. What is the Law of Sines?

The Law of Sines relates the lengths of sides of a triangle to the sines of its opposite angles. It's fundamental for solving triangles when you know either:

Where R is the radius of the triangle's circumscribed circle.

2. How Does the Calculator Work?

The calculator uses the Law of Sines combined with the Law of Cosines and angle sum property to determine unknown sides and angles.

Key formulas used:

• Law of Sines: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \)
• Law of Cosines: \( c^2 = a^2 + b^2 - 2ab\cos C \)
• Angle Sum: \( A + B + C = 180° \)

3. Triangle Solving Methods

Cases handled:

• SSS (three sides known)
• SAS (two sides and included angle)
• ASA (two angles and included side)
• AAS (two angles and non-included side)
• SSA (two sides and non-included angle - may have two solutions)

4. Using the Calculator

Instructions: Enter any three known values (sides and/or angles) of the triangle. The calculator will solve for the remaining values.

5. Frequently Asked Questions (FAQ)

Q1: What is the ambiguous case (SSA)?
A: When two sides and a non-included angle are known, there may be 0, 1, or 2 possible triangles.

Q2: How accurate are the calculations?
A: Results are accurate to within rounding errors. For critical applications, verify with alternative methods.

Q3: Can I use radians instead of degrees?
A: This calculator uses degrees. Convert radians to degrees by multiplying by 180/π.

Q4: What if my triangle is right-angled?
A: Right triangles can be solved more simply with Pythagorean theorem and basic trigonometry.

Q5: How do I know if my inputs form a valid triangle?
A: The calculator checks triangle inequality (sum of any two sides > third side) and angle sum (≈180°).