1. What is the Law of Sines?

The Law of Sines is a trigonometric equation relating the lengths of sides of a triangle to the sines of its opposite angles. It's particularly useful for solving triangles when you know two angles and one side (AAS or ASA cases).

2. How Does the Calculator Work?

The calculator uses the Law of Sines:

Where:

• \( a, b, c \) — Sides of the triangle (length units)
• \( A, B, C \) — Angles opposite to sides a, b, c respectively (degrees or radians)

Explanation: The ratio of each side to the sine of its opposite angle is constant for any given triangle.

3. When to Use AAS/ASA Calculation

Details: This method is used when you know:

• Two angles and any side (AAS)
• Two angles and the included side (ASA)

The third angle is always calculable since angles in a triangle sum to 180°.

4. Using the Calculator

Tips:

• Enter the known side length and two angles
• Specify which angle the side is opposite to
• Angles must be between 0-180 degrees
• Sum of two angles must be less than 180°

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between AAS and ASA?
A: AAS means two angles and a non-included side are known. ASA means two angles and the included side are known. Both can be solved similarly.

Q2: Can this solve right triangles?
A: Yes, but right triangles can also be solved using simpler Pythagorean theorem and basic trig ratios.

Q3: What if I get negative results?
A: Negative results indicate invalid input (angles summing to ≥180° or side length ≤0).

Q4: How precise are the results?
A: Results are rounded to 2 decimal places. For exact values, keep results in terms of sine functions.

Q5: Can I use radians instead of degrees?
A: The calculator currently uses degrees. Convert radians to degrees by multiplying by 180/π.