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The problem shows a right-angled triangle, where:

- The hypotenuse is 12 cm.
- One of the angles is 35°.
- We need to find the length of the side opposite to the right angle, denoted as \( x \).

### Step-by-step solution:

1. **Identify the trigonometric relation**:  
   Since we are given the hypotenuse (12 cm) and the angle (35°), and we are asked to find the adjacent side (denoted as \( x \)), the appropriate trigonometric function is **cosine**.

   \[
   \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
   \]
   where \( \theta = 35^\circ \), the adjacent side is \( x \), and the hypotenuse is 12 cm.

2. **Substitute the values into the formula**:

   \[
   \cos(35^\circ) = \frac{x}{12}
   \]

3. **Solve for \( x \)**:

   \[
   x = 12 \times \cos(35^\circ)
   \]

4. **Calculate the result**:

   Using a calculator or trigonometric table:

   \[
   \cos(35^\circ) \approx 0.8192
   \]

   Therefore:

   \[
   x = 12 \times 0.8192 \approx 9.83 \, \text{cm}
   \]

### Final Answer:
The value of \( x \) is approximately **9.83 cm**.

Would you like further explanation on any of the steps or more details?

Here are 5 related questions:
1. How would you solve for the opposite side in this triangle?
2. What trigonometric function relates the opposite side and the hypotenuse?
3. What is the value of \( \sin(35^\circ) \)?
4. How do we find the third angle in a right triangle?
5. How would the formula change if the given angle was at the adjacent side?

**Tip**: Always check whether you are solving for the opposite, adjacent, or hypotenuse when deciding which trigonometric function to use (sine, cosine, or tangent).

The diagram shows a right-angled triangle with the hypotenuse of 12 cm and one of the angles as 35°. Calculate the value of x (the adjacent side).

Learn how to calculate the adjacent side of a right-angled triangle given the hypotenuse and one angle (35°) using cosine. The solution involves applying the cosine formula: cos(35°) = adjacent / 12 cm. Suitable for students in Grades 9-10.

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