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To find \(\tan A\) for the given right triangle \(ABC\), we can use the definition of the tangent function in a right triangle:

\[
\tan \theta = \frac{\text{Opposite}}{\text{Adjacent}}
\]

Here, the angle \(A\) is at vertex \(A\). For angle \(A\):
- The **opposite side** is \(BC\), which has a length of 20.
- The **adjacent side** is \(AB\), which has a length of 21.

Therefore:

\[
\tan A = \frac{BC}{AB} = \frac{20}{21}
\]

So, \(\tan A = \frac{20}{21}\).

Would you like more details or have any questions?

Here are 8 related questions you might find useful:
1. How do you calculate the sine of angle \(A\) in this triangle?
2. How do you find the cosine of angle \(A\) in this triangle?
3. What is the value of \(\tan C\) in this triangle?
4. How do you calculate the hypotenuse if it wasn't given?
5. How do you solve for an angle given the tangent value?
6. What is the relationship between \(\tan A\) and \(\tan C\) in a right triangle?
7. How do you determine \(\sin A\) and \(\cos A\) using \(\tan A\)?
8. What would \(\tan A\) be if the triangle was isosceles with the same side lengths?

**Tip:** When working with trigonometric functions in right triangles, always make sure you correctly identify the sides relative to the angle of interest (opposite, adjacent, and hypotenuse).

Learn how to find the tangent of angle A in a right triangle ABC where the opposite side BC measures 20 units and the adjacent side AB measures 21 units. Detailed step-by-step solution provided.

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