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This image shows a right triangle where one leg has a length of 3, and the hypotenuse has a length of 10. The angle \( \theta \) is marked opposite the leg of length 3. To solve for \( \theta \), we can use trigonometric relationships.

Since the opposite leg is 3 and the hypotenuse is 10, we can use the sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{10}
\]
Now, let's calculate \( \theta \) using this relationship:

\[
\theta = \sin^{-1}\left(\frac{3}{10}\right)
\]

Let me calculate that for you.The angle \( \theta \) is approximately \( 17.46^\circ \).

Would you like further details, or do you have any other questions?

Here are 5 related questions you might find useful:
1. How do we find the length of the adjacent side in this triangle?
2. What other trigonometric ratios can we calculate for this triangle?
3. How can the Pythagorean theorem help confirm the side lengths?
4. What would the angle \( \theta \) be in radians?
5. How do we use the cosine function to calculate angles?

**Tip:** For triangles, always check if the triangle is right-angled to apply basic trigonometric ratios.

The figure is a right triangle. Give the exact value of the angle θ using the given side lengths: 3 (opposite) and 10 (hypotenuse).

Learn how to find the angle θ in a right triangle using trigonometric functions. Given an opposite side of 3 and a hypotenuse of 10, we calculate θ using the sine function and inverse trigonometry. Suitable for Grades 9-11.

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