Final answer:
The actual length of the 20 m tape is 20.015 m, as it measured a 100 m baseline to be 99.925 m in length. To accurately measure a 175.750 m line with this tape, one should measure 175.500 m to account for the tape's error.
Step-by-step explanation:
To find the actual length of the tape used in measuring the baseline, we can use the proportional error method. The observed length of the base was 99.925 m, which should have been precisely 100.000 m. Therefore, the actual length of the tape (T) can be found using the following equation:
Observed Length / Actual Length = Measured Length by the Tape / Tape's Actual Length
99.925 m / 100.000 m = 20 m / T
T = (20 m × 100.000 m) / 99.925 m
T = 20.015 m
Now, to lay out a 175.750 m line using this tape, we need to calculate the expected measured length (L) by compensating for the tape's error:
Actual Length to Measure / Tape's Actual Length = Measured Length / 20 m
175.750 m / 20.015 m = L / 20 m
L = (175.750 m × 20 m) / 20.015 m
L = 175.500 m
Therefore, when planning to measure 175.750 m with the tape that is 20.015 m long, one would actually measure a length of 175.500 m to get the accurate distance. The correct answers to the questions are 20.015 m for the actual length of the tape and 175.500 m for the distance that should be measured, which are not listed among the multiple-choice options provided.