✔ 最佳答案
1,A map of scale 1:100000 and AB=1.5 cm .If the actual length is 2.5km, find the difference in the heights between A and B.
horizontal distance between AB
=1.5*100000 cm
=150000 cm
=1500 m
=1.5 km
hypotenuse=actual length = 2.5km
So
(horizontal distance )^2+(height)^2=2.5^2
1.5^2+(height)^2=2.5^2
2.25+(height)^2=6.25
height=2 km
The heights between A and B is 2 km
2.On a map with the scale of 1:20000, a road of 3 km long is represented by a 14.4cm long line segment.What is the average gradient of the road?
First
The horizontal length of the road
=14.4 *20000 cm
=288000 cm
=2880 m
=2.8 km
actual length of the road (hypotenuse)= 3 km
Let x be the angle of elevation of the road from horizontal.
cos x = 2.88 km /3 km
x = 16.26'(cor. to 2 d.p.)
The average gradient of the road = tan a = 1 / (1 / tan a) = 1 : 3.43 (cor. to 3 sig. fig.)
