Math

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SSA Triangle Calculator.

Solve the ambiguous SSA case and report both valid solutions when they exist.

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Set your values

Results update as you type.

Result: angleB1: 22.02431284 · angleB2: undefined · sideC1: 12.61235091 · sideC2: undefined

Result

angleB1: 22.02431284 · angleB2: undefined · sideC1: 12.61235091 · sideC2: undefined

Use Cases

Check if a triangle is possible

Given two sides and a non-included angle, quickly see if a valid triangle exists and how many solutions there are.

Example: a=5, b=7, A=30° → two possible triangles.

Solve for missing angles and sides

Find the remaining angles and side for each possible triangle, useful in trigonometry homework or design.

Example: a=4, b=6, A=40° → compute B, C, and side c.

Frequently Asked Questions

What is the SSA triangle case?
SSA (side-side-angle) means you know two sides and a non-included angle. This can lead to zero, one, or two possible triangles, known as the ambiguous case.
How does the calculator determine the number of solutions?
It uses the given side a, side b, and angle A to compute the height and compare it with side a. If a is less than the height, no triangle; if equal, one right triangle; if greater but less than b, two triangles; otherwise one triangle.
What units are used for the input?
Sides a and b can be in any consistent unit (e.g., cm, m, inches). Angle A must be entered in degrees.

Tips & Common Mistakes

Tips

  • Ensure angle A is in degrees, not radians, for correct results.
  • Use consistent units for sides a and b (e.g., both in meters).
  • If you get two solutions, both are valid; check if your problem context restricts one.
  • Remember that the sum of angles in any triangle is 180°.

Common Mistakes to Avoid

  • Entering the angle in radians instead of degrees.
  • Mixing units for sides a and b (e.g., one in cm, the other in m).
  • Assuming there is always one solution; SSA can have zero, one, or two.

Last updated: August 13, 2026