The sight from A to the BM is a depression (-6°34'40''), giving V = -2.538 m. How is the axis RL of A found?

1200.000 + 2.843 + 2.538 = 1205.381 m (axis = RL BM + r - V)

1200.000 + 2.843 - 2.538 = 1200.305 m

1200.000 - 2.843 - 2.538 = 1194.619 m

The height of instrument at B is not given. What does the answer assume?

The axis of B is taken at the peg level; the true RL of T would change by the actual HI of B

HI of B is taken equal to that of A, so RL of T is unaffected

The axis of B is taken 1.518 m above the peg

RL of T does not depend on the axis of B

The elevation of T is 22°26'40'' from A and 27°32'40'' from B. Which statement is correct?

A is farther (smaller elevation); B lies between A and T, so x is A to T and B to T is x - D

B is farther from T, so x is measured from B

The two stations are equally distant from T

2078 Baisakh · 6 marks

RL of temple top from stations A and B

Short answer

Using stadia reduction, instrument axis RL at A is 1205.381 m and at B is 1207.243 m. Solving for horizontal distance from A to temple with elevation angles gives 71.696 m, so RL of temple top = 1234.997 m.

The top of a Temple (T) is sighted from two stations (A and B) at very different level, maintaining same vertical plane with the temple. Find the R.L. of the top of temple (T) from the following observed data:

Inst. Stn.	Target	Vertical Angle	Staff Reading	RL
A	Bench Mark (BM)	-6°34'40"	2.955, 2.843, 2.732	1200.00 m (BM)
	T (Temple)	22°26'40"
	B	10°21'50"	1.614, 1.518, 1.423
B	T (Temple)	27°32'40"

Assumptions: stadia constants $k = 100$ , $c = 0$ , staff vertical. The height of instrument at B is not given, so the axis of B is taken at the level of the peg B (the RL of T would change by the actual height of instrument at B). Distances are horizontal.

Step 1: RL of the axis of A (from the BM)

$s = 2.955 - 2.732 = 0.223$ m, $\theta = -6^\circ34'40''$
$V = \frac{ks}{2}\sin 2\theta = 50\times 0.223\times\sin(-13^\circ09'20'') = -2.538$ m
Axis of A $= RL_{BM} + r - V = 1200.000 + 2.843 - (-2.538) = 1205.381$ m

Step 2: distance AB and RL of axis at B

$s = 1.614 - 1.423 = 0.191$ m, $\theta = +10^\circ21'50''$
$D_{AB} = k s\cos^2\theta = 18.482$ m
$V = 50 s\sin2\theta = 3.380$ m
Ground at B $= 1205.381 + 3.380 - 1.518 = 1207.243$ m, so the axis of B is 1207.243 m (peg level).

Step 3: RL of the top T (A, B and T in one vertical plane, B between A and T)

Elevation angles of T: $\alpha_A = 22^\circ26'40''$ , $\alpha_B = 27^\circ32'40''$ . Let $x$ = horizontal distance A to T.

x = \frac{(axis_B - axis_A) - D\tan\alpha_B}{\tan\alpha_A - \tan\alpha_B} = \frac{(1207.243 - 1205.381) - 18.482\times 0.52155}{0.41308 - 0.52155} = 71.696\ \text{m}

RL_T = 1205.381 + 71.696\times 0.41308 = 1234.997\ \text{m}

Check from B: $1207.243 + (71.696 - 18.482)\times 0.52155 = 1234.997$ m.

Answer: RL of the top of the temple = 1234.997 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

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All Surveying II chapter 3 questions →

RL of temple top from stations A and B

Step 1: RL of the axis of A (from the BM)

Step 2: distance AB and RL of axis at B

Step 3: RL of the top T (A, B and T in one vertical plane, B between A and T)

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