1. What is the SSA Triangle Case?

The SSA (Side-Side-Angle) case occurs when we know two sides and a non-included angle of a triangle. This is known as the "ambiguous case" because it can result in zero, one, or two possible solutions.

2. How Does the Calculator Work?

The calculator uses the Law of Sines formula:

Where:

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

Explanation: The calculator checks if the solution exists (sin(B) ≤ 1) and whether a second solution is possible by considering the supplementary angle.

3. Understanding the Ambiguous Case

Details: The SSA case is called ambiguous because:

• No solution if side opposite is too short (a < b sinA)
• One right triangle solution if a = b sinA
• Two solutions if b sinA < a < b (acute and obtuse cases)
• One solution if a ≥ b

4. Using the Calculator

Tips: Enter side lengths (must be positive) and angle A (must be between 0° and 180°). The calculator will determine all possible solutions.

5. Frequently Asked Questions (FAQ)

Q1: Why is it called the ambiguous case?
A: Because given SSA information, there can be zero, one, or two possible triangles that satisfy the conditions.

Q2: When are there two solutions?
A: When side a is longer than b*sinA but shorter than side b (b sinA < a < b).

Q3: What's the difference between SSA and SAS?
A: SSA has the angle not included between the two sides, while SAS has the angle between the two known sides (which always gives one unique solution).

Q4: How accurate are the solutions?
A: Solutions are calculated to 2 decimal places. For precise calculations, exact values may be needed.

Q5: Can this be used for any triangle?
A: Yes, it works for acute, right, and obtuse triangles, provided you have the correct SSA information.