1. What is the Law of Sines Calculator?

Definition: This calculator finds an unknown side of a triangle when you know one side and its opposite angle, plus another angle.

Purpose: It helps solve oblique (non-right) triangles in trigonometry, navigation, surveying, and engineering applications.

2. How Does the Calculator Work?

The calculator uses the Law of Sines formula:

Rearranged to solve for side a:

Where:

• \( a \) — Unknown side length (meters)
• \( b \) — Known side length (meters)
• \( A \) — Angle opposite side a (degrees)
• \( B \) — Angle opposite side b (degrees)

3. When to Use the Law of Sines

Details: Use this method 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 known side length (must be > 0)
• Enter both angles in degrees (must be > 0 and sum < 180°)
• Angle A is opposite the unknown side you're calculating
• Angle B is opposite the known side you entered

5. Frequently Asked Questions (FAQ)

Q1: What if I have a right triangle?
A: For right triangles, use the Pythagorean theorem or basic trig ratios (SOHCAHTOA) instead.

Q2: Can I use this for all triangles?
A: Yes, the Law of Sines works for all triangles, but be cautious with the SSA (ambiguous) case.

Q3: What units should I use?
A: Any consistent length units (meters shown, but feet, inches, etc. work too). Angles must be in degrees.

Q4: Why does my calculation show an error?
A: Check that angles sum to less than 180° and all values are positive. The triangle must be possible.

Q5: How accurate is this calculation?
A: Very accurate when correct values are entered. Results are rounded to 3 decimal places.