To find the tangent of angle \( A \) in the right triangle \( \triangle ABC \), we use the definition of the tangent function in a right triangle. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.

In this case, for angle \( A \):

- The opposite side is \( BC = 1 \)
- The adjacent side is \( AC = 2 \)

Therefore, the tangent of angle \( A \) is:

\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AC} = \frac{1}{2}
\]

So, the tangent of angle \( A \) is \(\frac{1}{2}\).

Would you like more details or have any other questions? Here are some suggestions for further exploration:

1. How do you find the sine and cosine of angle \( A \)?
2. What is the length of the altitude from point \( C \) to the hypotenuse \( AB \)?
3. How can you find the coordinates of the points \( A \), \( B \), and \( C \) if you place \( C \) at the origin?
4. What are the other trigonometric ratios (cotangent, secant, cosecant) for angle \( A \)?
5. How do you find the area of triangle \( \triangle ABC \) using its side lengths?

**Tip:** For right triangles, using the basic trigonometric ratios (sine, cosine, tangent) can help solve many geometric problems efficiently.

Learn how to find the tangent of angle A in a right triangle with BC = 1 and AC = 2 using the tangent function formula. Understand the basic trigonometric ratios and their application in geometry. Suitable for high school students.

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