The image shows a right triangle with sides labeled 20, 29, and an angle $\theta$. You are asked to find $\sin(\theta)$.

To calculate $\sin(\theta)$:

• The sine of an angle in a right triangle is given by the formula: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

• In this case, $\theta$ is adjacent to the side with length 20, meaning that the side opposite to $\theta$ is the one with length 20. The hypotenuse is the longest side, which is 29.

Thus: $\sin(\theta) = \frac{20}{29}$

So, the correct answer is: $\sin(\theta) = \frac{20}{29}$

Let me know if you'd like further clarification or details!

Here are 5 related questions for practice:

1. What is $\cos(\theta)$ for the same triangle?
2. Can you calculate $\tan(\theta)$ using the given sides?
3. If $\sin(\theta) = \frac{20}{29}$, what is $\sin(90^\circ - \theta)$?
4. How can you verify the Pythagorean theorem using the given triangle sides?
5. What is the approximate value of $\sin(\theta)$ in decimal form?

Tip: Always remember that the hypotenuse is the longest side in a right triangle, which simplifies identifying the opposite and adjacent sides.