To solve the equation $\frac{x}{6} = \sin(38^\circ)$:

Step-by-step solution:

1. Start with the given equation: $\frac{x}{6} = \sin(38^\circ)$

2. Calculate $\sin(38^\circ)$: $\sin(38^\circ) \approx 0.6157$

3. Substitute the value of $\sin(38^\circ)$ back into the equation: $\frac{x}{6} = 0.6157$

4. Multiply both sides of the equation by 6 to solve for $x$: $x = 6 \times 0.6157$

5. Perform the multiplication: $x \approx 3.6942$

Final Answer:

$x \approx 3.6942$

Would you like further details or have any questions? Here are some related questions to deepen your understanding:

1. How is the sine of an angle calculated in a right triangle?
2. What is the unit circle definition of sine?
3. How can we solve trigonometric equations involving cosine or tangent?
4. What happens if the angle is given in radians instead of degrees?
5. Can the sine of an angle ever be greater than 1?

Tip: Always make sure your calculator is set to the correct mode (degrees or radians) when working with trigonometric functions.