What formula represents the area of an oblique triangle?

The area of an oblique triangle can be calculated using the formula that involves two sides and the sine of the included angle between them. The formula is given by:

Area = 1/2 * a * b * sin(C)

In this case, the parameters a and b represent the lengths of two sides of the triangle, while C is the included angle between those two sides. This formula is derived from the general concept of the area of a triangle, which is dependent on the base and height. When using sine, the height can be expressed as one of the sides multiplied by the sine of the included angle.

While the correct answer involves angle C, it is important to recognize that the use of sin in the area formula is crucial because it takes into account the orientation of the triangle. Thus, the formula captures how the angle affects the height relative to the base formed by the two sides.

In contrast, formulas that involve cos or tan of an angle would not appropriately represent the area of the triangle. Cosine functions relate more to adjacent sides and do not account for the height necessary for area calculation, while tangent angles do not directly relate to area in this context. Overall, the correct use of the sine function with the included angle ensures an