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The question asks to find the cosine of the angle \( \theta \) in a right triangle. The side lengths provided are 29 (the hypotenuse), 20 (the adjacent side to \( \theta \)), and 21 (the opposite side to \( \theta \)).

According to the cosine function, using the mnemonic **SOHCAHTOA**:
- **Cosine** (cos) is the ratio of the adjacent side to the hypotenuse:
\[
\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{20}{29}
\]

Now, calculating the decimal value:
\[
\cos(\theta) = \frac{20}{29} \approx 0.6897
\]

Rounding to the nearest hundredth:
\[
\cos(\theta) \approx 0.69
\]

Thus, the value of \( \cos(\theta) \) is approximately **0.69**.

Would you like further explanation or details on this? Here are some related questions:

1. How would you calculate \( \sin(\theta) \) for the same triangle?
2. What is the tangent of \( \theta \) using the given side lengths?
3. Can the Pythagorean theorem confirm the side lengths are correct?
4. What is the relationship between the three trigonometric functions?
5. How would you solve for an angle given a cosine ratio?

**Tip:** Always check that the adjacent side and hypotenuse are correctly identified when using cosine.

Find the trigonometric ratio cos(θ) for a right triangle with side lengths 29 (hypotenuse), 20 (adjacent side), and 21 (opposite side).

Learn how to find the cosine of an angle in a right triangle with side lengths 29 (hypotenuse), 20 (adjacent), and 21 (opposite). This step-by-step guide explains the cosine function, SOHCAHTOA, and provides the solution to the problem.

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