GATE 2024 MN – Question 48
From P, a vertical staff at A has bearing 145°, vertical angle+8° and readings 1.2, 1.7, 2.2 m; B has bearing 205°, angle+3° and readings 0.8, 1.2, 1.6 m. Tacheometer constants are K 100, C 0. Find horizontal AB in m, to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 88.50 to 91.50
Explanation
For a vertical staff and zero additive constant, horizontal distance is Ks cos²θ. Thus PA = 100×1.0×cos²8° = 98.0631 m and PB = 100×0.8×cos²3° = 79.7809 m. Their bearing difference is 205°−145° = 60°. The cosine rule gives AB = √(PA²+PB²−2PA·PB cos 60°) = 90.3205 m, or 90.32 m. Central readings affect elevations rather than these horizontal distances.