Which triangle's area can be calculated using the trigonometric area formula $A=\frac{1}{2}absinC$?

• A. A triangle where only one side and one angle are known (SA case)
• B. A triangle where all three sides are known (SSS case)
• C. A triangle where two sides and the included angle are known (SAS case)
• D. A triangle where all three angles are known (AAA case)

Answer: (C)

Verified step by step guidance

1. Understand the trigonometric area formula for a triangle: \(A = \frac{1}{2}ab\sin C\), where \(a\) and \(b\) are two sides of the triangle and \(C\) is the included angle between those sides.
2. Recognize that this formula requires knowledge of two sides and the angle between them, which corresponds to the SAS (Side-Angle-Side) case.
3. Note that if only one side and one angle are known (SA case), you do not have enough information to apply this formula directly because you need two sides.
4. If all three sides are known (SSS case), you would typically use Heron's formula instead of the trigonometric area formula.
5. If all three angles are known (AAA case), the triangle's size is not determined (only shape), so the area cannot be calculated without at least one side length.