https://file.aiquickdraw.com/mathbot/file/17274477869942e99qahr.jpg

To solve for \( \tan X \) in the triangle shown, we use the definition of the tangent function in a right triangle:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

For angle \( X \), the side opposite to \( X \) is \( 32 \), and the side adjacent to \( X \) is \( 24 \).

Thus, 

\[
\tan X = \frac{32}{24} = \frac{4}{3}
\]

The correct answer from the options is:

\[
\boxed{32/24}
\]

Would you like more details or have any questions about this?

Here are 5 related questions:
1. How do you find the sine and cosine of angle \( X \) in this triangle?
2. What is the value of \( \tan^{-1}(4/3) \) in degrees or radians?
3. How does the Pythagorean theorem apply to this triangle?
4. What is the hypotenuse of the triangle using the given sides?
5. How do you apply trigonometry to solve for unknown angles in a triangle?

**Tip:** Always remember that tangent is the ratio of the opposite side to the adjacent side when dealing with right triangles.

Find tan(X) for a right triangle with an opposite side of 32 and an adjacent side of 24.

Solve for tan(X) in a right triangle where the opposite side is 32 and the adjacent side is 24. This problem uses basic trigonometry formulas and is suitable for students in Grades 9-10.

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