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 works for any triangle, not just right-angled ones.

2. How Does the Calculator Work?

The calculator uses the Law of Sines:

Where:

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

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

3. When to Use the Law of Sines

Details: Use this law when you know:

• Two angles and one side (AAS or ASA cases)
• Two sides and an angle opposite one of them (SSA case)

4. Using the Calculator

Tips: Enter any three elements (sides or angles) of the triangle. The calculator will solve for the remaining elements. Angles must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Law of Sines and Law of Cosines?
A: Law of Sines relates sides to opposite angles, while Law of Cosines relates all three sides to one angle (better for SAS or SSS cases).

Q2: What is the ambiguous case (SSA)?
A: When given two sides and a non-included angle, there may be 0, 1, or 2 possible solutions.

Q3: Can I use this for right triangles?
A: Yes, but right triangles have simpler trigonometric relationships (SOHCAHTOA).

Q4: What units should I use?
A: Any consistent units for sides (cm, m, inches). Angles must be in degrees (0-180°).

Q5: How accurate are the results?
A: Results are mathematically precise, though real-world measurements have their own accuracy limits.