Question 1

What is the Law of Sines formula?

Accepted Answer

The Law of Sines states that the ratio of each side length to the sine of its opposite angle is constant: a / sin(A) = b / sin(B) = c / sin(C) = 2R, where R is the circumradius.

Question 2

What is the ambiguous case (SSA) in trigonometry?

Accepted Answer

When two sides and a non-included angle are known (SSA), there may be zero, one, or two valid triangles depending on whether side a is less than, equal to, or greater than altitude h = b * sin(A).

Question 3

When should you use the Law of Cosines instead?

Accepted Answer

Use the Law of Cosines when you know three sides (SSS) or two sides and the included angle (SAS), where the Law of Sines lacks sufficient known opposite pairs to initiate calculations.

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