https://file.aiquickdraw.com/mathbot/file/17267371803824h9guinl.jpg

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!

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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.

What is the value of sin(θ) in the right triangle with sides 20, 29, and θ?

This problem involves finding the sine of an angle (θ) in a right triangle with side lengths 20, 29. Learn how to use the sine formula and apply basic trigonometry concepts. Suitable for high school students (Grades 9-12).

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