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

$ \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