1. What is the Law of Sines?

The Law of Sines is a trigonometric formula relating the lengths of sides of a triangle to the sines of its opposite angles. It's useful for finding unknown angles or sides in any triangle.

2. How Does the Calculator Work?

The calculator uses the Law of Sines formula:

Where:

• \( A \) — Unknown angle (degrees or radians)
• \( a \) — Length of side opposite angle A
• \( B \) — Known angle (degrees or radians)
• \( b \) — Length of side opposite angle B

Explanation: The formula calculates angle A when you know side a, side b, and angle B. The result can be in degrees or radians.

3. Importance of Angle Calculation

Details: Calculating triangle angles is essential in geometry, navigation, engineering, and physics. It helps determine the shape and dimensions of triangular structures.

4. Using the Calculator

Tips: Enter side lengths in any consistent units. Angle B must be between 0 and 180 degrees (or 0 and π radians). The ratio (a·sin(B)/b) must be between -1 and 1.

5. Frequently Asked Questions (FAQ)

Q1: When can't the Law of Sines be used?
A: It can't be used when you only know the three sides (SSS) or two sides and their included angle (SAS). Use Law of Cosines in these cases.

Q2: What is the ambiguous case?
A: When given SSA (two sides and a non-included angle), there may be two possible solutions, one solution, or no solution.

Q3: Can I use this for right triangles?
A: Yes, but right triangles can be solved more simply with basic trigonometric functions (sine, cosine, tangent).

Q4: What units should I use for sides?
A: Any consistent units (cm, m, inches, etc.) as long as both sides use the same unit.

Q5: How precise are the results?
A: Results are precise to two decimal places. For exact values, consider exact trigonometric solutions.