The length and bearings of a traverse PQRS are Segment Length(m) Bearing PQ 40 80° QR 50 10° RS 30 210° The length of line segment SP (in m, round off to two decimal places), is

GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

Question : 65 of 65

Marks: +1, -0

The length and bearings of a traverse PQRS are

The length of line segment SP (in m, round off to two decimal places), is

Solution:

Segment	Length	Bearing	Lat.(lcosθ)	Dep. (lsinθ)
PQ	40	80	6.945	39.392
QR	50	10	49.250	8.682
RS	30	210	–25.980	–15
SP	l	θ	Icosθ	lsinθ

Σ L=\cos θ+30.215=0

Σ D=I \sin θ+33.081=0

l\cos θ=-30.215

l\sin θ=-33.081

I=√{(30.215)^{2}+(33.081)^{2}}

I=44.802 {m}

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