1. What is the Law of Sines?

The Law of Sines is a trigonometric formula that relates the lengths of sides of a triangle to the sines of its opposite angles. It's particularly useful for solving triangles when you know either:

• Two angles and one side (AAS or ASA cases)
• Two sides and one non-included angle (SSA case)

2. How Does the Calculator Work?

The calculator uses the Law of Sines formula:

Rearranged to solve for the unknown side:

Where:

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

3. When to Use This Calculation

Applications: This calculation is essential in trigonometry, navigation, surveying, and engineering when you need to determine unknown sides of a triangle based on angle measurements.

4. Using the Calculator

Tips: Enter the known side length in meters, the angle opposite the unknown side in degrees, and the angle opposite the known side in degrees. All angles must be between 0-180° and their sum must be less than 180°.

5. Frequently Asked Questions (FAQ)

Q1: What if I know two sides and an included angle?
A: Use the Law of Cosines instead, which is better suited for SAS (side-angle-side) cases.

Q2: How accurate is this calculation?
A: The calculation is mathematically exact, but practical accuracy depends on the precision of your angle and side measurements.

Q3: Can this be used for any triangle?
A: Yes, the Law of Sines works for all triangles (acute, right, and obtuse).

Q4: What if I get an error message?
A: Check that your angles sum to less than 180° and all values are positive numbers.

Q5: Can I calculate angles with this formula?
A: Yes, the Law of Sines can be rearranged to find angles if you know two sides and one opposite angle.