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標題:

mathematics (Trigonometry)

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發問:

1. On a map with the scale of 1:20000, a road of 3km long is represented by a 14.4 cm long line segment. What is the average gradient of the road?

最佳解答:

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

其他解答:

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)5AEEC82B53E1B405