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To solve the problem, we need to find the length of side \( b \) in a right triangle where:

- \( C = 90^\circ \)
- \( A = 37^\circ \)
- Hypotenuse \( c = 88 \) cm

Since this is a right triangle, we can use trigonometric functions. Given the angle \( A = 37^\circ \) and hypotenuse \( c \), we can use the cosine function to find side \( b \), which is adjacent to angle \( A \).

### Step-by-step Solution:

1. **Identify the Formula**:
   \[
   \cos(A) = \frac{\text{adjacent side (b)}}{\text{hypotenuse (c)}}
   \]

2. **Substitute the Given Values**:
   \[
   \cos(37^\circ) = \frac{b}{88}
   \]

3. **Solve for \( b \)**:
   \[
   b = 88 \times \cos(37^\circ)
   \]

4. **Calculate the Value**:
   \[
   b \approx 88 \times 0.7986 = 70.2768
   \]

5. **Round to the Nearest Whole Number**:
   \[
   b \approx 70 \text{ cm}
   \]

### Answer:
The length of side \( b \) is approximately **70 cm**.

Would you like more details or have any other questions?

Here are 5 related questions to further expand on this topic:

1. How do you find the length of the other leg in a right triangle given one leg and the hypotenuse?
2. What is the sine of an angle in a right triangle and how can it be used to find missing sides?
3. How can the Pythagorean Theorem be applied to solve problems involving right triangles?
4. How would you solve for the remaining angle \( B \) in this triangle?
5. What is the tangent function and how is it used in solving right triangle problems?

**Tip**: When working with trigonometric functions, make sure your calculator is set to the correct mode (degrees or radians) based on the given problem.

If A = 37° and c = 88 cm, find b in a right triangle where C = 90°.

Learn how to find the length of side b in a right triangle where A = 37° and hypotenuse c = 88 cm. This trigonometry problem uses the cosine formula to calculate the missing side. Suitable for students in Grades 9-11.

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