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To find the measure of angle \( \angle B \) (denoted as \( m\angle B \)) in the given right triangle \( \triangle ABC \), we can use trigonometric functions. Here’s how:

### Step 1: Identify the sides
In the right triangle \( ABC \):
- \( AB = 25 \) (Opposite side relative to \( \angle B \))
- \( BC = 30 \) (Hypotenuse)

### Step 2: Use the sine function
The sine of angle \( B \) is given by:
\[
\sin B = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{AB}{BC} = \frac{25}{30}
\]

### Step 3: Calculate \( \sin B \)
\[
\sin B = \frac{25}{30} = \frac{5}{6} \approx 0.8333
\]

### Step 4: Find \( \angle B \) using the inverse sine function
\[
B = \sin^{-1}(0.8333)
\]

### Step 5: Calculate the angle
Using a calculator or trigonometric tables:
\[
B \approx \sin^{-1}(0.8333) \approx 56.4^\circ
\]

Thus, the measure of angle \( B \) is approximately **56.4°** to the nearest tenth.

Would you like any further details or have any questions?

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Here are 5 related questions:
1. How can we use the cosine function to find \( m\angle A \) in the same triangle?
2. What is the measure of angle \( C \) in \( \triangle ABC \)?
3. Can we use the tangent function to find \( m\angle B \)? If so, how?
4. How do you determine which trigonometric function to use based on given sides?
5. How does the Pythagorean theorem confirm the accuracy of the given side lengths?

**Tip:** For solving right triangles, always check if you can apply the Pythagorean theorem before using trigonometric functions. This can help verify that the triangle sides are correct.

Learn how to calculate the measure of angle B in a right triangle with side lengths 25 and 30 using sine and inverse trigonometric functions. Suitable for students in Grades 9-10.

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