1. What is the Law of Sines Calculator?

Definition: This calculator solves triangles using the Law of Sines, which relates the lengths of sides to the sines of their opposite angles.

Purpose: It helps find missing sides or angles in any triangle when you know at least one side-angle pair plus one other element.

2. How Does the Calculator Work?

The calculator uses the Law of Sines formula:

Where:

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

Explanation: The ratio of any side length to the sine of its opposite angle is constant for all three sides of the triangle.

3. When to Use the Law of Sines

Details: Use this calculator 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) with at least one side. The calculator will determine the remaining elements.

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.

Q2: Does this work for all triangles?
A: Yes, the Law of Sines works for all triangles (acute, right, and obtuse).

Q3: What if I get two possible solutions?
A: The SSA case (two sides and non-included angle) can sometimes produce two valid triangles (the "ambiguous case").

Q4: How accurate are the results?
A: Results are accurate to 3 decimal places, but real-world measurements may have limitations.

Q5: Can I use this for right triangles?
A: Yes, but the Pythagorean theorem might be simpler for right triangles.