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 triangles depending on the given values.

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
• \( B \) — Angle to be calculated

Explanation: The calculator determines all possible triangles that satisfy the given SSA conditions, checking for the ambiguous case where two solutions might exist.

3. Understanding the Ambiguous Case

Details: The ambiguous case occurs when:

• Side opposite the given angle is shorter than the other given side
• The given angle is acute
• The calculated sin(B) value is valid (between -1 and 1)

In these cases, there may be two possible triangles, one acute and one obtuse.

4. Using the Calculator

Tips: Enter side lengths as positive numbers and angle A between 0 and 180 degrees. The calculator will show all possible solutions or indicate if no triangle exists with the given measurements.

5. Frequently Asked Questions (FAQ)

Q1: When does the SSA case have no solution?
A: When \( b \sin A > a \), meaning the side is too short to reach the opposite side, forming no triangle.

Q2: When is there exactly one solution?
A: When \( a \geq b \) or when \( \sin B = 1 \) (right triangle case).

Q3: How can there be two solutions?
A: When \( b \sin A < a < b \) and angle A is acute, both an acute and obtuse triangle may satisfy the conditions.

Q4: Why is it called the ambiguous case?
A: Because the given information may correspond to two different triangles, one triangle, or no triangle at all.

Q5: Does this work for any triangle?
A: Yes, but results are most meaningful for oblique triangles (non-right triangles).