Solve a triangle when two sides and a non-included angle (SSA) are known.
Known Dimensions
°
Triangle Analysis
2
Possible Solutions
Results obtained via the Law of Sines, accounting for the ambiguous case.
Triangle 1
Angle B38.7°
Angle C111.3°
Side c22.36
Triangle 2
Angle B141.3°
Angle C8.7°
Side c3.62
About this calculator
What is the SSA Case?
The Side-Side-Angle (SSA) case is known as the 'ambiguous case' in trigonometry. Given two sides and a non-included angle, there could be zero, one, or two distinct triangles that satisfy the given conditions.
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Pro Tips
If (b · sin A) > a, no triangle exists.
If a ≥ b, only one triangle exists.
If (b · sin A) < a < b, two different triangles are possible.
A right triangle exists if a = b · sin A.
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Fun Facts
"SSA is not a valid congruence theorem because of its ambiguity."
"Navigators must be careful with SSA to avoid plotting the wrong destination."
"The ambiguity arises because the sine function from 0° to 180° is symmetrical around 90°."
