1. The problem asks to find the value of the trigonometric ratio \( \tan A \) given the sides 20 and 21. 2. Recall the definition of tangent in a right triangle: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \). 3. Here, \( \tan A = \frac{20}{21} \). 4. This fraction cannot be simplified further, so the value of \( \tan A \) is \( \frac{20}{21} \). Final answer: \( \tan A = \frac{20}{21} \).