https://file.aiquickdraw.com/mathbot/file/17268457810207bgd22kb.jpg

The image shows a right triangle \( \triangle ABC \) with a right angle at \( C \). The sides are labeled as follows:

- \( AB = 29 \) (the hypotenuse),
- \( BC = 20 \),
- \( AC = 21 \),
- and angle \( \alpha \) is at vertex \( A \).

The question asks to find \( \cos(\alpha) \).

In a right triangle, the cosine of an angle is given by:

\[
\cos(\alpha) = \frac{\text{adjacent side to } \alpha}{\text{hypotenuse}}.
\]

For \( \alpha \), the adjacent side is \( BC = 20 \), and the hypotenuse is \( AB = 29 \). Thus:

\[
\cos(\alpha) = \frac{20}{29}.
\]

Therefore, the correct answer is option **D**: \( \frac{20}{29} \).

Would you like further details or have any questions?

Here are five related questions to explore further:
1. How do you find \( \sin(\alpha) \) in this triangle?
2. What is the value of \( \tan(\alpha) \) using the triangle's sides?
3. How do you use the Pythagorean theorem to verify the triangle's side lengths?
4. What is the complementary angle to \( \alpha \) in this triangle?
5. How does the cosine rule differ from basic trigonometric definitions in right triangles?

**Tip:** In right triangles, knowing two sides is enough to compute all trigonometric functions for any non-right angle.

Encontre cos(α) no triângulo. Escolha a resposta correta entre: 21/29, 21/20, 20/21, ou 20/29.

Learn how to find cos(α) in a right triangle with sides AB = 29, BC = 20, and AC = 21. This trigonometry problem demonstrates how to calculate the cosine of an angle using the formula cos(α) = adjacent/hypotenuse. Perfect for students in Grades 9-10.

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