PR^2 = 5^2 + 4^2 - 2*5*4*cos 135
=25 + 16 - 40(-.707)
= 69.28
so
PR = 8.32
sin RPQ / 4 = sin 135 /8.32
so
sin angle RPQ = .34
Angle RPQ = 19.9 deg
Angle SPR = 90 - 19.9 = 70.1 deg
RS^2 = 3^2 + 8.32^2 - 2 *3 *8.32 cos 70.1
= 9 + 69.2 - 17 = 61.2
so
RS = 7.82 cm = 0.0782 meters
* 4000 = 313 meters
a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle.
(b) The quadrilateral PQRS represents a plot of land drawn to a scale of l: 4000. Determine the actual length of RS in meters.
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