GATE 2020 CE (CE1) – Question 65
Traverse PQRS has lengths and whole-circle bearings: PQ 40 m at 80°, QR 50 m at 10°, RS 30 m at 210°. Find closing segment SP length (m), to two decimals.
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Correct answer: 44 to 45
Explanation
Signed northing sum is $40\cos80^\circ+50\cos10^\circ+30\cos210^\circ=30.205553$ m. Easting sum is $40\sin80^\circ+50\sin10^\circ+30\sin210^\circ=33.074719$ m. Closing SP has opposite components and length $\sqrt{N^2+E^2}=\mathbf{44.79}$ m.