Which formula is used to find the area of a triangle when two sides and the included angle are known (SAS case)?

• A. $abc$
• B. $\frac{1}{2}ab$
• C. $\frac{1}{2}absinC$
• D. $\frac{1}{2}acsinB$

Answer: (C)

Verified step by step guidance

1. Recall that the area of a triangle can be found using different formulas depending on the known elements. When two sides and the included angle (SAS case) are known, we use a specific trigonometric formula.
2. Identify the two known sides, say \(a\) and \(b\), and the included angle between them, say \(C\).
3. The formula for the area in this case is given by multiplying half the product of the two sides by the sine of the included angle.
4. Write the formula as: \(\text{Area} = \frac{1}{2} \times a \times b \times \sin C\).
5. This formula works because the height of the triangle relative to one side can be expressed using the sine of the included angle, effectively giving the area without needing the height explicitly.