This problem refers to right triangle ABC with 
C = 90°.
 Begin the problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately.

If 
b = 8.9 mm and c = 12 mm,
 find B. (Round your answer to the nearest whole number.)
B =

We are given a right triangle \( \triangle ABC \), with the following information:

- Angle \( C = 90^\circ \), meaning it's a right triangle.
- Side \( b = 8.9 \, \text{mm} \), which is the leg adjacent to angle \( B \).
- Side \( c = 12 \, \text{mm} \), which is the hypotenuse.

We are asked to find angle \( B \).

### Step 1: Use the cosine formula
In a right triangle, the cosine of an angle \( B \) is the ratio of the adjacent side (side \( b \)) to the hypotenuse (side \( c \)):

\[
\cos(B) = \frac{b}{c}
\]

Substitute the given values:

\[
\cos(B) = \frac{8.9}{12}
\]

\[
\cos(B) \approx 0.7417
\]

### Step 2: Find angle \( B \)
Now, take the inverse cosine (arccos) of 0.7417 to find \( B \):

\[
B = \cos^{-1}(0.7417)
\]

Let's calculate that.

\[
B \approx 42^\circ
\]

### Final Answer:
Angle \( B \) is approximately \( 42^\circ \).

---

Would you like further details or have any questions? Here are five related questions:

1. What is angle \( A \) in the triangle if \( B = 42^\circ \)?
2. How would you calculate the missing side \( a \) in the triangle?
3. What trigonometric function relates angle \( B \) to the opposite side \( a \)?
4. How do you verify the sum of angles in a right triangle?
5. How would the problem change if side \( a \) were given instead of \( b \)?

**Tip:** When solving for angles in a right triangle, always ensure you're using the correct trigonometric ratio based on the sides involved (adjacent, opposite, or hypotenuse).

This problem refers to right triangle ABC with C = 90°. Begin the problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. If b = 8.9 mm and c = 12 mm, find B. (Round your answer to the nearest whole number.) B = 

Solve for angle B in a right triangle ABC where C = 90°, b = 8.9 mm, and c = 12 mm using trigonometric ratios. Learn how to apply the cosine function and find the angle using the inverse cosine. This problem is suitable for students in Grades 8-10.

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