To determine the most probable value of an angle measured by different observers, we can use the method of averaging the observed values. Let's calculate the average of the given measurements:
1st measurement: 74° 39' 45" (1 time)
2nd measurement: 74° 39' 45" (1 time)
3rd measurement: 74° 39' 27" (4 times)
4th measurement: 74° 39' 35" (6 times)
To calculate the average, we need to convert all the measurements to a common unit, such as degrees:
1st measurement: 74° 39' 45" = 74 + (39/60) + (45/3600) = 74.6625°
2nd measurement: 74° 39' 45" = 74 + (39/60) + (45/3600) = 74.6625°
3rd measurement: 74° 39' 27" = 74 + (39/60) + (27/3600) = 74.6575°
4th measurement: 74° 39' 35" = 74 + (39/60) + (35/3600) = 74.6597°
Now, let's calculate the average:
Average = (74.6625° + 74.6625° + 74.6575° + 74.6597°) / (1 + 1 + 4 + 6)
Simplifying this expression will give us the most probable value of the angle.