In a right triangle, the two non-right angles, \( A \) and \( C \), are complementary. That is, \( A + C = 90^\circ \). For complementary angles in a right triangle, the sine of one angle is equal to the cosine of the other angle.
Given:
1. \(\sin(A) = \frac{24}{25}\)
2. \(\cos(C) = \frac{20}{20}\)
Step-by-Step Solution:
1. \(\sin(A) = \frac{24}{25}\):
- Since \( A \) and \( C \) are complementary angles, \(\cos(C) = \sin(A)\).
- Therefore, \(\cos(C) = \frac{24}{25}\).
2. \(\cos(C) = \frac{20}{20}\):
- Simplify \(\frac{20}{20}\): \(\frac{20}{20} = 1\).
- Since \( A \) and \( C \) are complementary angles, \(\sin(A) = \cos(C)\).
- Therefore, \(\sin(A) = 1\).
Thus:
[tex]\[
\cos(C) = \frac{24}{25}
\][/tex]
[tex]\[
\sin(A) = 1
\][/tex]
