A right triangle [tex]\( ABC \)[/tex] has complementary angles [tex]\( A \)[/tex] and [tex]\( C \)[/tex].
1. To determine the value of [tex]\(\cos(C)\)[/tex] when [tex]\(\sin(A) = \frac{24}{25}\)[/tex]:
- Since [tex]\( A \)[/tex] and [tex]\( C \)[/tex] are complementary angles, we know that [tex]\( \sin(A) = \cos(C) \)[/tex].
- Thus, if [tex]\(\sin(A) = \frac{24}{25}\)[/tex], then [tex]\(\cos(C) = \frac{24}{25}\)[/tex].
2. To determine the value of [tex]\(\sin(A)\)[/tex] when [tex]\(\cos(C) = \frac{20}{29}\)[/tex]:
- Similarly, since [tex]\( A \)[/tex] and [tex]\( C \)[/tex] are complementary angles, we know that [tex]\( \cos(C) = \sin(A) \)[/tex].
- Thus, if [tex]\(\cos(C) = \frac{20}{29}\)[/tex], then [tex]\(\sin(A) = \frac{20}{29}\)[/tex].
Therefore, the values are:
[tex]\[
\cos(C) = 0.96
\][/tex]
[tex]\[
\sin(A) = 0.6896551724137931
\][/tex]