A horizontal angle was measured by repetition six times with a total station. If the initial display reading was 21o33'18" and the final reading was 129o20'04", determine the value of the angle to the nearest second.

The value of the angle is 107° 46' 46''

Explanation:

we know that

To find out the value of the angle, subtract the initial display reading from the final reading

Remember that

1°=60'

1'=60''

1°=3,600''

we have

Initial display reading=21° 33' 18''

Convert to seconds

21 (3,600) + 33 (60) + 18=77,598''

Final display reading=129° 20' 04''

Convert to seconds

129 (3,600) + 20 (60) + 4=465,604''

Find the difference

465,604''-77,598''=388,006''

Convert 388,006'' to degrees

388,006''/3,600=107.7794°

Convert 0.7794° to minutes

0.7794 (60) = 46.764'

Convert 0.764' to seconds

0.764 (60) = 45.84''=46''

therefore

The value of the angle is

107° 46' 46''