Final answer:
The distance between the Moon and Earth can be found using the concept of arc length. By applying the formula for arc length and substituting the given values, the distance is approximately 384,070,796.4 meters.
Step-by-step explanation:
To find the distance between the moon and the Earth, we can use the concept of arc length. The subtended angle of 0.00904 radians on Earth's surface corresponds to an arc length equal to the moon's diameter, which is 3.47x10^6 meters.
The formula for arc length is given by:
arc length = radius * subtended angle
Since the moon's diameter is twice its radius, we can rewrite the formula as:
arc length = 2 * radius * subtended angle
Substituting the given values, we have:
3.47x10^6 m = 2 * radius * 0.00904 rad
Solving for the radius, we get:
radius = 3.47x10^6 m / (2 * 0.00904 rad)
Therefore, the distance between the moon and the Earth is twice the radius:
distance = 2 * radius
distance = 2 * 3.47x10^6 m / (2 * 0.00904 rad)
distance = 3.47x10^6 m / 0.00904 rad
distance ≈ 384,070,796.4 meters