To find the value of $x$, we can use trigonometry, specifically the sine function, since we have a right triangle, the hypotenuse, and an angle.

Step-by-Step Solution:

1. Identify the known values:

   • Angle: $45^\circ$
   • Hypotenuse: 600 units
   • Opposite side (which is $x$): Unknown

2. Apply the sine function: $\sin(45^\circ) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{x}{600}$

3. Solve for $x$: $x = 600 \times \sin(45^\circ)$

4. Calculate the sine of 45°: $\sin(45^\circ) = \frac{\sqrt{2}}{2} \approx 0.7071$

5. Plug this value into the equation: $x = 600 \times 0.7071 \approx 424.26 \text{ units}$

6. Round to the nearest hundredth: $x \approx 424.26 \text{ units}$

Final Answer:

The value of $x$ is approximately 424.26 units.

Would you like further details or have any other questions? Here are some related questions that might interest you:

1. How would the value of $x$ change if the hypotenuse was 800 units instead of 600?
2. What is the effect on $x$ if the angle is changed to 30°?
3. How would you find the hypotenuse if $x$ was given and the angle was 60°?
4. Can you calculate $x$ using the cosine function if the adjacent side was given instead?
5. How can you find the adjacent side given the hypotenuse and the angle?

Tip: When dealing with right triangles, it's helpful to remember that the sine of an angle gives you the ratio of the opposite side to the hypotenuse, while the cosine gives the ratio of the adjacent side to the hypotenuse.