mathematics (Trigonometry)

1: 20000, that is 1 cm. : 20,000 cm = 200m
so 14.4 cm. = 200 x 14.4 = 2880 m = 2.88 km.
Let x be the angle of the slope, so cos x = 2.88/3. x = arccos(2.88/3) = 16.26 degree.
so average gradient = tan 16.26 = 0.29 = 1 : 3.45

If the gradient of the road is 0 , it should be represented by a

3*100000 / 20000 = 15 cm long line segment.

So the average gradient of the road = [(15^2 - 14.4^2)^ 1/2] / 14.4

= 4.2 / 14.4

= 7 / 24


2009-11-02 22:04:40 補充：
i.e.

= 1 : (24/7)

= 1 : 3.42857142...

= 1 : 3.43#(3 sig. figure)