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

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

In this triangle:
- The side opposite angle \(\beta\) is \(8\) (side \(AC\)),
- The side adjacent to angle \(\beta\) is \(15\) (side \(BC\)).

Thus:

\[
\tan(\beta) = \frac{8}{15}
\]

The correct answer is **A: \(\frac{8}{15}\)**.

Would you like further details on this explanation? Here are some related questions you might find helpful:

1. What is the relationship between sine, cosine, and tangent in a right triangle?
2. How do you find the hypotenuse of a triangle using the Pythagorean theorem?
3. How do you convert between degrees and radians when working with angles?
4. What is the cosine of angle \(\beta\) in this triangle?
5. How would you calculate the sine of angle \(\beta\) in this triangle?

**Tip:** In trigonometry, always remember that the tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.

Encontre tg(β) no triângulo dado, com lados de 8, 15 e 17.

Learn how to calculate the tangent of angle β in a right triangle with sides of 8, 15, and 17. This problem uses key trigonometric concepts, including the tangent function and Pythagorean theorem. Suitable for students in Grades 9-11.

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