1. What is the Law of Sines Calculator?

Definition: This calculator solves for unknown sides or angles in a triangle using the Law of Sines formula.

Purpose: It helps in trigonometry problems where you know either two sides and one angle or two angles and one side.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Length of side opposite angle A (meters)
• \( b \) — Length of side opposite angle B (meters)
• \( A \) — Angle opposite side a (degrees)
• \( B \) — Angle opposite side b (degrees)

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

3. Importance of Law of Sines

Details: The Law of Sines is essential for solving oblique triangles (non-right triangles) in navigation, surveying, and physics problems.

4. Using the Calculator

Tips: Enter any three known values (two sides and one angle or two angles and one side). The calculator will solve for the remaining value.

5. Frequently Asked Questions (FAQ)

Q1: What if I get an error message?
A: Ensure you've entered exactly three known values and that the values follow triangle rules (angles sum to 180°).

Q2: Can this solve for all triangle cases?
A: It solves ASA, AAS, and SSA cases. For SSS cases, use the Law of Cosines.

Q3: What about side c and angle C?
A: After finding two angles, subtract from 180° to get the third angle. Then use Law of Sines again to find the third side.

Q4: Why might there be two solutions?
A: In the SSA case (ambiguous case), there can be two possible triangles. The calculator will show both solutions if they exist.

Q5: How precise are the results?
A: Results are accurate to 3 decimal places, but real-world measurements may have different precision.