An astronaut is working on a satellite 200 miles above the ground. What is the measure of BD⌢, the portion of Earth that the astronaut can see? Round your answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)

To find the measure of BD⌢, you can use the formula for the arc length of a circle: \( \text{Arc Length} = 2\pi r \left( \frac{\theta}{360} \right) \), where \( r \) is the radius and \( \theta \) is the central angle in degrees.

The astronaut's line of sight forms a central angle at the center of the Earth. Since the satellite is 200 miles above the ground, the radius for this calculation is \( 4000 + 200 = 4200 \) miles.

The central angle is formed by the astronaut's line of sight, which is a right triangle with the hypotenuse being the radius plus the height of the satellite. You can use trigonometry to find this angle: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).

Let \( x \) be the length of BD⌢. Then \( \sin(\theta) = \frac{x}{4200} \).

Once you find \( \theta \), you can use it in the arc length formula to find the measure of BD⌢. Round your answer to the nearest tenth.