# GATE Papers >> Civil >> 2019 >> Question No 53

Question No. 53

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 __________

##### Answer : 100 to 100

Solution of Question No 53 of GATE 2019 Civil Paper

$\mathrm{tanθ}=\frac{2.4-\mathrm x}{50}=\frac{\mathrm x-0.4}{50}$

2x = 2.8

x = 1.4m

H.O.I = 100 + 1.4 = 101.4m

RL of theodelite station = 101.4 - theodelite hight = 101.4 - 1.4 = 100m