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The sine of a 45-degree angle in a right triangle is:

\[
\sin(45^\circ) = \frac{1}{\sqrt{2}} \approx 0.7071
\]

This result comes from the properties of a 45-45-90 triangle, where the legs are equal, and the hypotenuse is \(\sqrt{2}\) times the length of either leg.

Would you like a more detailed explanation or have further questions? Here are five related questions:

1. What is the cosine of a 45-degree angle in a right triangle?
2. How do you derive the sine of a 45-degree angle using the unit circle?
3. What is the sine of other common angles like 30° or 60°?
4. Why are the sine and cosine of 45 degrees equal?
5. How can you use trigonometry to solve for unknown sides in a right triangle?

**Tip**: In trigonometry, using reference triangles like the 45-45-90 triangle can help you memorize the values of sine, cosine, and tangent for standard angles.

What is the sine of a 45-degree angle in a right triangle?

Learn how to find the sine of a 45-degree angle in a right triangle. This problem covers trigonometric concepts, including the properties of a 45-45-90 triangle and the sine formula. Suitable for students in Grades 9-12.

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