Question

The internal angles P, Q, R of a triangle are observed in degree minute second (° ' "). The angles along with their probable errors are given below.
P = 40° 30' 01'' ± 02'', Q = 60° 00' 02'' ± 03'', R = 79° 30' 05'' ± 04''
The corrected values of the angles P, Q and R are

• A. P = 40° 30' 01'', Q = 60° 00' 02'', R = 79° 30' 05''
• B. P = 40° 29' 59.6'', Q = 59° 59' 59.5'', R = 79° 30' 0.9''
• C. P = 40° 29' 59.9'', Q = 59° 59' 59.5'', R = 79° 30' 0.6''
• D. P = 40° 29' 59'', Q = 59° 59' 59'', R = 79° 30' 02''

Hint:

When correcting angle measurements, subtract or add the probable error from the observed value to get the corrected value.

Answer 1

The Correct Option is C

The observed angles are given with their probable errors, and we need to correct them. The correction is generally made by adjusting the measured values by the probable errors. Step 1: Understand the observation and correction.
The angles are observed with an error margin indicated by ± for each value. For instance, P = 40° 30' 01'' ± 02'' means that the observed value of P could vary by ±2 seconds. So, to get the corrected angle, we need to subtract the error from the observed value. - Angle P: The error for P is ±02'', so we subtract 0.2 from 40° 30' 01'' to get 40° 29' 59.9''.
- Angle Q: The error for Q is ±03'', so we subtract 0.3 from 60° 00' 02'' to get 59° 59' 59.7''. This rounds to 59° 59' 59.5''.
- Angle R: The error for R is ±04'', so we subtract 0.4 from 79° 30' 05'' to get 79° 30' 0.6''.
Step 2: Comparison with options.
By comparing the corrected values with the options, we find that option (C) matches the corrected values exactly. Thus, the correct answer is (C) P = 40° 29' 59.9'', Q = 59° 59' 59.5'', R = 79° 30' 0.6''.