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The given triangle is a right-angled triangle, where:

- One side (opposite to the angle \(\theta\)) is 10 cm,
- The other side (adjacent to \(\theta\)) is 12 cm.

We can use trigonometric functions to calculate the size of \(\theta\). Specifically, the tangent function relates the opposite and adjacent sides:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{10}{12} = \frac{5}{6}
\]

To find \(\theta\), take the inverse tangent (arctan or \(\tan^{-1}\)):

\[
\theta = \tan^{-1}\left(\frac{5}{6}\right)
\]

I'll calculate this next.

\[
\theta \approx \tan^{-1}(0.8333) \approx 39.81^\circ
\]

Thus, the size of angle \(\theta\) is approximately **39.81°**.

Would you like more details or have any further questions?

Here are 5 relative questions based on this:

1. How would you calculate the hypotenuse in this right triangle?
2. What trigonometric function could you use to find angle \(\theta\) using the hypotenuse?
3. How would you calculate the remaining angle in the triangle?
4. What are the key differences between sine, cosine, and tangent functions in right triangles?
5. How would the value of \(\theta\) change if the adjacent side were shorter?

**Tip:** Always remember that in right-angled triangles, the tangent function helps to relate the opposite and adjacent sides directly.

What is the size of angle θ in a right triangle with opposite side of 10 cm and adjacent side of 12 cm?

Learn how to calculate the angle θ in a right triangle with an opposite side of 10 cm and an adjacent side of 12 cm using the tangent function. Step-by-step solution with explanations, perfect for students in Grades 8-10.

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