Question

A tacheometer was placed at point P to estimate the horizontal distances PQ and PR. The corresponding stadia intercepts with the telescope kept horizontal are 0.320 and 0.210 m respectively. The $\angle$QPR is measured to be ${61}^{\circ }{30}^{\prime }{30}^{\prime \prime }$ . If the stadia multiplication constant = 100 and stadia addition constant = 0.10 m. The horizontal distance (in m) between the points Q and R is____

• A. 28.8

Answer 1

The correct option is A 28.8
Given:

K = 100

C = 0.10 m

We know that,

horizontal distance is equal to k.S. + C . where S is staff intercept.

$\therefore$ PQ = K .(s) + C

$=100\cdot \left(0.320\right)+0.10$

= 32.1 m

Similarly, $PR=100\times 0.21+0.1$

= 21.1m

By cosine law,

$QR=\sqrt{P{Q}^2+P{R}^2-2\times PQ\times PRcos{60}^{\circ }30{}^{\prime }30{{}^{\prime }}^{\prime }}$

= 28.799

$\simeq$ 28.8 m