Final answer:
Option 2) sin(a) = h/c represents a true sine ratio for angle 'a' in a triangle abc, where 'h' is the side opposite angle 'a' and 'c' is the hypotenuse, assuming the traditional notation of sides in a triangle.
Step-by-step explanation:
The student has asked which equation represents a true sine ratio in a triangle labeled abc. To determine the correct sine ratio, we refer to the definition of the sine function in a right triangle. The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, the correct sine ratio for an angle 'A' in a right triangle is sin(A) = opposite/hypotenuse.
Looking at the given options:
- Option 1) sin(a) = b/c is incorrect because 'b' is not necessarily the side opposite angle 'a' and 'c' is not necessarily the hypotenuse.
- Option 2) sin(a) = h/c is correct if 'h' represents the side opposite angle 'a' and 'c' is the hypotenuse.
- Option 3) sin(c) = b/a is incorrect as it implies side 'b' is the hypotenuse and side 'a' is opposite angle 'c', which is not the definition of the sine.
- Option 4) sin(c) = a/h is incorrect if 'h' is the hypotenuse and 'a' is the side opposite angle 'c', since this is in fact the definition of cosine, not sine.
Therefore, Option 2) represents a true sine ratio, assuming that 'h' is the length of the side opposite angle 'a' and 'c' is the length of the hypotenuse. However, we must clarify that in the context of the question, 'h' must be the opposite side of angle 'a' for this to be true.