Parallax Angle:
The parallax angle is the angle formed between the line of sight from two different locations to an object. In the case of the moon, the parallax angle is used to determine its distance from the Earth.

Given Information:
- Distance between two places on Earth = 6.4 × 10^6 m
- Parallax angle = 57 minutes of an arc

Parallax Angle Calculation:
To calculate the distance of the moon from Earth, we need to first convert the parallax angle from minutes of an arc to radians.

1 degree = 60 minutes
1 radian = 180/π degrees

Therefore, 1 minute of an arc = (1/60) degrees = (1/60) * (180/π) radians

Given parallax angle = 57 minutes of an arc
Parallax angle in radians = (57/60) * (180/π) radians

Distance Calculation:
The distance between the two locations on Earth forms a baseline for the parallax angle calculation. The moon is at an angle between the two lines of sight from the two locations.

Using the concept of triangulation, we can determine the distance to the moon using the parallax angle and the baseline distance.

The formula to calculate distance is:
Distance to the moon = Baseline Distance / tan(Parallax Angle)

Substituting the values:
Baseline Distance = 6.4 × 10^6 m
Parallax Angle = (57/60) * (180/π) radians

Distance to the moon = (6.4 × 10^6 m) / tan((57/60) * (180/π) radians)

Calculating the distance:
Using the given values, we can substitute them into the formula and calculate the distance to the moon.

After performing the calculations, the distance to the moon from Earth is found to be approximately 3.84 × 10^8 meters.

Conclusion:
The distance of the moon from Earth, determined using the parallax angle measured from two locations at a distance of 6.4 × 10^6 m on Earth, is approximately 3.84 × 10^8 meters. The parallax angle is crucial in determining the distance to celestial objects and is an important tool in astronomical measurements.

The ans. is 107.27×10^3 km