https://file.aiquickdraw.com/mathbot/file/1725845274753xey6l157.jpg

The image shows a right-angled triangle with sides labeled. Let's identify the key details:

- The triangle \( \triangle ABC \) has:
  - \( AB = 5 \) (blue side, adjacent to angle \( \theta \)),
  - \( AC = 3 \) (red side, opposite angle \( \theta \)),
  - \( BC = 7 \) (hypotenuse).

The problem asks to find the value of \( \cos \theta \), where \( \theta \) is the angle at vertex \( A \).

### Solution:
The cosine of an angle \( \theta \) in a right triangle is given by:
\[
\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Here:
- The adjacent side is \( AB = 5 \),
- The hypotenuse is \( BC = 7 \).

Thus:
\[
\cos \theta = \frac{5}{7}
\]

The value of \( \cos \theta \) is \( \frac{5}{7} \).

Would you like further details, or do you have any questions?

Here are some related questions:
1. How do we calculate \( \sin \theta \) for this triangle?
2. What is the value of \( \tan \theta \)?
3. How can we verify the triangle's side lengths using the Pythagorean theorem?
4. What is the significance of the angle \( \theta \) in trigonometry?
5. Can we find the angle \( \theta \) using inverse cosine?

**Tip:** Always remember that in a right triangle, the cosine function relates the adjacent side to the hypotenuse!

Tentukan nilai cos θ dari gambar berikut!

Learn how to find the cosine of an angle θ in a right-angled triangle with side lengths 3, 5, and 7. This problem covers trigonometric concepts, including the cosine formula and the Pythagorean theorem. Suitable for students in Grades 7-9.

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