We are given a right triangle with the side opposite angle A having a length of 76 and the hypotenuse having a length of 95.
The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this case, $\sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{76}{95}$.
\\(\boxed{\sin A = \frac{76}{95}}\\)
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