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To find angle \( B \) in the given right triangle \( \triangle ABC \), where \( \angle A \) is the right angle, we can use trigonometric ratios. Given:

- \( AB = 25 \) (adjacent side to angle \( B \))
- \( AC = 30 \) (hypotenuse)

We can use the cosine function, defined as:
\[ \cos(B) = \frac{\text{adjacent}}{\text{hypotenuse}} \]

Thus,
\[ \cos(B) = \frac{AB}{AC} = \frac{25}{30} = \frac{5}{6} \]

Now, to find angle \( B \), we take the inverse cosine (arccos):
\[ B = \arccos\left(\frac{5}{6}\right) \]

Using a calculator to find the arccos:
\[ B \approx \arccos\left(\frac{5}{6}\right) \approx 33.56^\circ \]

So, angle \( B \) is approximately \( 33.56^\circ \).

Would you like further details or have any questions about this solution?

Here are some related questions you might find interesting:

1. How can we find angle \( C \) in the triangle?
2. What is the sine of angle \( B \)?
3. How can we use the Pythagorean theorem to verify the side lengths?
4. What is the tangent of angle \( B \)?
5. How do we calculate the area of \( \triangle ABC \)?

**Tip:** For right triangles, using trigonometric ratios (sine, cosine, tangent) is a straightforward way to find angles when side lengths are known.

Learn how to find angle B in the right triangle ABC using trigonometric ratios. This problem involves using the cosine function and inverse cosine (arccos) to determine the angle. Suitable for high school students studying trigonometry.

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