Given that \( A \) and \( C \) are complementary angles in a right triangle, we know that \( A + C = 90^\circ \). This implies that \( \sin(A) = \cos(C) \) and \( \cos(A) = \sin(C) \).
1. If \(\sin (A) = \frac{24}{25}\):
Since \( A \) and \( C \) are complementary angles, \(\cos (C)\) is equal to \(\sin (A)\).
Therefore, \(\cos (C) = \frac{24}{25}\).
So, the value of \(\cos (C)\) is \( \boxed{\frac{24}{25}} \).
2. If \(\cos (C) = \frac{20}{29}\):
Again, because \( A \) and \( C \) are complementary angles, \(\sin (A)\) is equal to \(\cos (C)\).
So, \(\sin (A) = \frac{20}{29}\).
Thus, the value of [tex]\(\sin (A)\)[/tex] is [tex]\( \boxed{\frac{20}{29}} \)[/tex].
