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.