https://file.aiquickdraw.com/mathbot/file/1727455897056cpdu004k.jpg

The triangle in the image is a right triangle with one side labeled 9, the hypotenuse labeled 19, and an unknown angle \( x^\circ \) opposite the side of length 9. To find \( x^\circ \), we can use trigonometry, specifically the sine function, since sine relates the opposite side to the hypotenuse in a right triangle:

\[
\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{9}{19}
\]

Now, solving for \( x \):

\[
x = \arcsin\left(\frac{9}{19}\right)
\]

Let me calculate that for you.The angle \( x^\circ \) is approximately \( 28.27^\circ \).

Do you have any further questions or would you like more details?

Here are some related questions you might find useful:
1. How do you calculate angles in a right triangle using trigonometric ratios?
2. What is the relationship between sine, cosine, and tangent in trigonometry?
3. How can you solve for unknown sides in a right triangle using trigonometry?
4. What other functions could you use to find angle \( x \) if you had different sides?
5. How does the Pythagorean theorem apply to right triangles?

**Tip:** Always ensure your calculator is set to the correct mode (degrees or radians) based on the problem requirements when solving trigonometric functions.

Find the unknown angle x in the right triangle with sides 9 and hypotenuse 19.

Learn how to calculate the unknown angle x in a right triangle using trigonometry. With a side of 9 and a hypotenuse of 19, we apply the sine function to find the angle. Suitable for high school students, covering core trigonometric concepts.

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