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 oblique triangles (non-right triangles).

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 the length of a side to the sine of its opposite angle is constant for all three sides and angles in a triangle.

3. Applications of Oblique Triangle Calculations

Details: Used in navigation, surveying, astronomy, and various engineering fields where precise distance or angle measurements are needed.

4. Using the Calculator

Tips: Enter any three elements (sides or angles) with at least one side. The calculator will determine the remaining elements. Angles must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the minimum information needed to solve a triangle?
A: You need at least three elements including at least one side (SSS, SAS, ASA, AAS, or SSA configurations).

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

Q3: Can I use this for right triangles?
A: Yes, though right triangles can be solved more simply with Pythagorean theorem and basic trigonometric functions.

Q4: What units should I use?
A: Any consistent units for sides (cm, m, km, etc.). Angles must be in degrees.

Q5: What if my angles don't add up to 180°?
A: The calculator will adjust the third angle to ensure the sum is exactly 180°.