Question

32. The correction to be applied to each
30m chain length along a slope, is
a) 30(seco - 1)m
b) 30(sine - 1)m
c)30(COSO - 1)m
d)30(tane - 1)m​

Answer 1

a) 30(sec θ - 1)m

Step-by-step explanation:

30m as the horizontal distance and find the sloping distance for that.

AB' cos (θ) = 30

AB' = 30 /cos(θ),

AB' = 30 sec (θ)

Hypotenuse allowance (HA) = the distance BB' we have to mark ahead of B so that the measured length along the slope is the true horizontal distance.

HA = AB - AB'

= 30 × sec(θ) - 30,

= 30 [sec (θ) - 1]

Answer 2

Step-by-step explanation:

For surveying the distance we need is the horizontal distance. But for sloping grounds, we can't directly measure the horizontal distance.

So we will measure the sloping distance and apply the correction (by knowing the slope). We are doing it

(i) either by measuring the full sloping distance once and applying the correction at the office later by using trigonometric relations,

(ii) or we will apply corrections at each chain length so that we don't have to do any corrections at the office. Keep in mind this much.

Here we are using the second method.

Suppose we are measuring a single chain distance L from A to B along a slope of 'theta' degree,

AB = L metre.

The TRUE horizontal distance for this AB is Lcos(theta), which will be less than L metre.

So what we do is we will mark a point B' whose TRUE length is L metre, which is ahead of actual measured point B. Then we will start the next chain from the point B' instead of B.

For that, we take Lm as the horizontal distance and find the sloping distance for that.

AB'cos (θ) = L

AB' = L /cos(θ),

AB' = L sec (θ).

Hypotenusal allowance (HA) = the distance BB' we have to mark ahead of B so that the measured length along the slope is the true horizontal distance.

HA = AB - AB'

= L.sec(θ) - L,

= L [sec (θ) - 1].