mathematics (Trigonometry)
2009-11-03 5:25 am
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?
回答 (2)
2009-11-03 5:49 am
✔ 最佳答案
1: 20000, that is 1 cm. : 20,000 cm = 200mso 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
2009-11-03 5:38 am
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)
收錄日期: 2021-04-21 22:05:47
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091102000051KK01486