The bearings of two inaccessible stations, S1 (Easting 500

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The bearings of two inaccessible stations, S₁ (Easting 500 m, Northing 500 m) and S₂ (Easting 600 m, Northing 450 m) from a station S₃ were observed as 225° and 153° 26' respectively. The independent Easting (in m) of station S₃ is :

1. 450.000
2. 570.710
3. 550.000
4. 650.000

Correct Option: C

Northing of S₃ = 500 + L₁ cos 45°
= 450 + L₂ cos 26° 34'
⇒ L₁ cos 45° – L₂ cos26° 34' = –50
Easting of S₃
= 500 + L₁ sin 45° = 600 – L₂ sin 26° 34'
L₁ sin 45° + L₂ sin 26°34' = 100
∴ L₁ = 70.71, L₂ = 111.80
Easting of S₃ = 500 + 70.71 × sin 45° ≈ 550m