What does the area formula 1/2absinC require from a triangle?

The area formula ( \frac{1}{2}ab\sin C ) is specifically designed for finding the area of a triangle when two sides and the included angle are known. Here, ( a ) and ( b ) represent the lengths of the two sides, while ( C ) is the angle that lies between those sides.

This formula derives from the relationship between the sides of the triangle and the sine of the angle. It effectively calculates the area by considering the base formed by one of the sides and the height inferred from the angle, which is projected onto the other side. This means that knowing the lengths of both sides and the angle between them is sufficient to compute the area, rather than needing the height or the length of the third side.

In contrast, the area formula does not require a right angle, as it is applicable to all types of triangles, nor does it require the lengths of all three sides, or just the base and height. Therefore, the correctness of the statement hinges on the necessity of having the two sides and the included angle to use this specific formula for area calculation.