To find the measure of angle \( A \) in a right triangle where the adjacent side is 25 and the opposite side is 20, we can use the tangent function:
\[ \tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{20}{25} \]
Simplifying this gives:
\[ \tan(A) = \frac{4}{5} \]
Now, to find angle \( A \), we take the arctangent (inverse tangent) of \( \frac{4}{5} \):
\[ A = \tan^{-1}\left(\frac{4}{5}\right) \]
Using a calculator to compute this:
\[ A \approx 38.66 \text{ degrees} \]
Rounding to the nearest whole number, we find:
\[ \boxed{39} \]
So, the measure of angle \( A \) is approximately 39 degrees.
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