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.
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
To determine the actual length of RS in meters, we need to use the given scale of the plot, which is 1:4000.
First, let's calculate the length of RS in centimeters. Since we have the lengths of PQ and QR, we can find RS by subtracting the length of QR from the length of PQ (RS = PQ - QR).
RS = PQ - QR = 5 cm - 4 cm = 1 cm
Now, we need to convert this length from centimeters to meters using the scale factor of 1 meter = 100 cm.
1 cm = 1/100 meters
Therefore, the actual length of RS is:
RS = 1 cm * (1/100) meters = 0.01 meters
So, the actual length of RS in meters is 0.01 meters.