Question

An instrument is set up at a station P and the angle of depression to a vane, 1.20 m above the foot of the staff held at Q is 5°. The horizontal distance PQ is observed to be 300 m. The R.L. of point Q is __________________ m (round off to 3 decimal places). Given that the staff reading at a BM (Elevation 436.050 m) is 2.865 m.

Hint:

When calculating R.L. using the angle of depression, remember to subtract the height of the instrument and the correction for the distance and angle.

Answer 1

Correct Answer: 411

To find the R.L. of point Q, we can use the formula involving the angle of depression: \[ \text{R.L. of Q} = \text{R.L. of P} - h - d \times \tan(\theta) \] Where:
- \( \theta \) is the angle of depression (5°),
- \( h \) is the height of the instrument above the staff (1.20 m),
- \( d \) is the horizontal distance (300 m),
- R.L. of point P is the staff reading at the BM, \( 436.050 - 2.865 = 433.185 \, \text{m} \).
Now, substitute the values into the equation: \[ \text{R.L. of Q} = 433.185 - 1.20 - 300 \times \tan(5^\circ) = 433.185 - 1.20 - 300 \times 0.08749 = 433.185 - 1.20 - 26.247 = 405.738 \, \text{m} \] Final Answer: \[ \boxed{405.738 \, \text{m}} \]