One angle in a right triangle measures `y ^(@)` such that cos `y ^(@) = (24)/(25).` What is the measure of `sin (90^(@)-y ^(@))` ?

Answer

To solve the problem, we need to find the value of \( \sin(90^\circ - y) \) given that \( \cos(y) = \frac{24}{25} \).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
We know from trigonometric identities that:
\[ \sin(90^\circ - y) = \cos(y) \]
This is a fundamental property of trigonometric functions.

2. **Substituting the Given Value**:
Since we are given \( \cos(y) = \frac{24}{25} \), we can substitute this value into the identity:
\[ \sin(90^\circ - y) = \cos(y) = \frac{24}{25} \]

3. **Final Answer**:
Therefore, the measure of \( \sin(90^\circ - y) \) is:
\[ \sin(90^\circ - y) = \frac{24}{25} \]