To solve the equation \( \sin(23.4^\circ) = \frac{19}{x} \), we can rearrange it to find \( x \):

1. First, calculate \( \sin(23.4^\circ) \):
   \[
   \sin(23.4^\circ) \approx 0.3978
   \]

2. Substitute this value into the equation:
   \[
   0.3978 = \frac{19}{x}
   \]

3. Cross-multiply to solve for \( x \):
   \[
   0.3978x = 19
   \]
   \[
   x = \frac{19}{0.3978} \approx 47.7
   \]

Thus, \( x \approx 47.7 \).

Would you like any further details or explanations? Here are some related questions you might find interesting:

1. What is the range of the sine function?
2. How can you find the sine of angles greater than 90 degrees?
3. What is the relationship between sine and the unit circle?
4. Can you provide examples of other trigonometric equations?
5. How does the sine function behave in different quadrants?

**Tip:** Always check your calculator's mode (degrees vs. radians) when calculating trigonometric functions!

Learn how to solve the trigonometric equation sin(23.4°) = 19/x by finding the value of x using cross-multiplication and sine calculations. This step-by-step solution covers key trigonometric concepts, suitable for high school students in Grades 10-12.

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