A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite is placed at a horizontal distance of 50 m from the BM to measure the vertical angles

Q. A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite is placed at a horizontal distance of 50 m from the BM to measure the vertical angles. The measured vertical angles from the horizontal at the staff readings of 0.400 m and 2.400 m are found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the theodolite station is ______                   

Solution:

tan θ=2.4−x/50=x−0.4/50

2x=2.8

x=1.4 m

H.O.I. =100+1.4

=101.4 m

RL of theodolite station = 101.4 – Theodolite height

=101.4−1.4

=100 m