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 scalene (unequal) triangles where no angle is 90°.

2. How Does the Calculator Work?

The calculator uses the Law of Sines:

Where:

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

Explanation: The ratio of each side to the sine of its opposite angle is equal for all three sides and angles in any triangle.

3. Importance of Triangle Calculations

Details: Solving triangles is fundamental in geometry, physics, engineering, and navigation. The Law of Sines is essential when dealing with non-right-angled triangles.

4. Using the Calculator

Tips: Enter any three known values (sides or angles) to calculate the remaining unknowns. At least one side-length must be known. Angles must be in degrees (0-180°).

5. Frequently Asked Questions (FAQ)

Q1: What is a scalene triangle?
A: A triangle where all sides have different lengths and all angles have different measures.

Q2: Can I use this for right triangles?
A: Yes, but the Pythagorean theorem is typically simpler for right triangles.

Q3: What if I get NaN or errors?
A: Check that your inputs form a valid triangle (sum of angles = 180°, sides satisfy triangle inequality).

Q4: How precise are the results?
A: Results are rounded to 2 decimal places. For exact values, symbolic computation may be needed.

Q5: What about the ambiguous case (SSA)?
A: The calculator returns one solution. There may be two possible triangles in some SSA cases.