Question

Which of the following cannot be derived from the law of sines?

A) b / sinB = sinA / a
B) a · sinB = b · sin A
C) sin C / sin A = c / a
D) c · sin A = a · sinC

Answer 1

The equation that cannot be derived from the law of sines is c · sin A = a · sinC (option D).

Step-by-step explanation:

The law of sines states that in any given triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Using this law, we can derive equations such as:

1. a / sinA = b / sinB: This equation can be derived from the law of sines as it represents the ratio between the lengths of two sides of a triangle and the sines of their opposite angles.
2. a · sinB = b · sin A: This equation can also be derived from the law of sines as it represents the product of a side length and the sine of its opposite angle.
3. sin C / sin A = c / a: This equation can be derived from the law of sines as it represents the ratio between the sines of two angles and the ratio between the lengths of their opposite sides.

Therefore, the equation that cannot be derived from the law of sines is c · sin A = a · sinC (option D).