Question

The lengths and bearing of a traverse PQRS are:

Segment	Length(m)	Bearing
PQ	40	${80}^{\circ }$
QR	50	${10}^{\circ }$
RS	30	${210}^{\circ }$

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

• A. 44.79

Answer 1

The correct option is A 44.79

$\sum L=PQ\cos {80}^{\circ }+QR\cos {10}^{\circ }+RS\cos {210}^{\circ }+SP\cos \theta =0$
$\sum L=40\cos {80}^{\circ }+50\cos {10}^{\circ }+30\cos {210}^{\circ }+SP\cos \theta =0$
$SP\cos \theta =-30.205$
$\sum D=PQ\sin {80}^{\circ }+QR\sin {10}^{\circ }+RS\sin {210}^{\circ }+SP\sin \theta =0$
$SP\sin \theta =-33.074$
$SP=\sqrt{(SP\cos \theta {)}^2+(SP\sin \theta {)}^2}$
$SP=44.791m$