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In this question, we have a right-angled triangle \( \triangle ABC \), with:

- \( \angle ACB = 35^\circ \)
- Side \( BC = 20 \, \text{cm} \) (the adjacent side to the angle)
- Side \( AB \) is the side to be calculated (opposite side)

We can use the **tangent** trigonometric function, which relates the opposite side and the adjacent side in a right-angled triangle:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

For \( \theta = 35^\circ \), \( \text{opposite} = AB \), and \( \text{adjacent} = BC = 20 \, \text{cm} \), the formula becomes:

\[
\tan(35^\circ) = \frac{AB}{20}
\]

Now we solve for \( AB \):

\[
AB = 20 \times \tan(35^\circ)
\]

Let's calculate the value of \( AB \).The length of side \( AB \) is approximately \( 14.00 \, \text{cm} \).

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. How do you calculate the hypotenuse in a right triangle if you know two sides?
2. What is the relationship between sine and cosine in right triangles?
3. Can you calculate the area of this triangle?
4. How do you find the other angle in a right-angled triangle?
5. What is the difference between adjacent and opposite sides in trigonometry?

**Tip:** Always make sure your calculator is in the correct mode (degrees or radians) when working with trigonometric functions!

Calculate the length AB in the triangle where angle ACB = 35°, BC = 20 cm, and triangle ABC is right-angled.

Learn how to calculate the length of side AB in a right-angled triangle where angle ACB is 35° and side BC is 20 cm using the tangent function. This step-by-step solution includes key trigonometric formulas suitable for Grades 9-10.

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