1. What is the Ambiguous Case (SSA)?

The SSA (Side-Side-Angle) case is called ambiguous because when two sides and a non-included angle are given, there can be 0, 1, or 2 possible triangles that satisfy the given conditions.

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
• \( A \) — Given angle in degrees

Explanation: The calculator determines how many triangles can be formed based on the relationship between the given sides and angle.

3. Possible Solutions

Details: The number of possible triangles depends on:

• No solution if \( b \sin A > a \)
• One solution if \( b \sin A = a \) (right triangle) or if \( b \geq a \)
• Two solutions if \( b \sin A < a \) and \( b < a \)

4. Using the Calculator

Tips: Enter side lengths a and b (must be positive), and angle A (must be between 0° and 180°). The calculator will determine how many triangles can be formed with these measurements.

5. Frequently Asked Questions (FAQ)

Q1: Why is the SSA case ambiguous?
A: Because with two sides and a non-included angle, there can be different configurations that satisfy the given measurements.

Q2: How can I visualize the ambiguous case?
A: Imagine swinging side b from angle A - it might not reach side a (no solution), just touch it (one solution), or intersect it at two points (two solutions).

Q3: Does this work for all triangles?
A: This specifically applies to the SSA case. Other combinations (SAS, ASA, SSS) always have exactly one solution.

Q4: What if I get two solutions?
A: Both solutions are mathematically valid. Additional context would be needed to determine which one applies to your specific situation.

Q5: Can this calculator handle obtuse angles?
A: Yes, the calculator works for acute and obtuse angles (up to 180°).