richiesmasher
Junior Member
- Joined
- Dec 15, 2017
- Messages
- 111
Find angle of latitude: distance between P (63° N, 70°E), R (63° N, x° E) is 900km
Hi I've done a question on latitude and longitude.
It states : Take the radius of the earth to be 6400km and pi to be 3.142.
(i)The distance between Town P (63° N, 70°E) and Town R (63° N, x° E) is 900km.
If Town R is east of Town P, determine x°E, the longitude of R, to one decimal place.
Now I've done this using this formula: let (c) be the circumference of the parallel of latitude, and (C) be the circumference of the earth.
So I know that c = C*cos(theta)
C is = 40217.6km
And the length of the arc of latitude QY is : l=c*(a/360)
so : 900km=40217.6km *cos63° *a/360
a= (900*360)/(40217.6*cos63°)
a= 17.7
So I would have thought that now all I had to do was subtract this from the angle of longitude I have 70° but apparently its when I add 17.7° to 70° I get x = 87.7° which is the answer, this I don't understand as all the other examples in my book subtract.
Now for the second part of the question, this I'm stuck like Ive never been before.
''The shortest distance between Town P (63° N,70° E) and Town Q (y° N, 110° W) is 6702.9km
Determine y° N, the latitude of Q. (The answer is 57° if this helps anyone) I have no clue how to do this.
Here is a picture attached of how I got part (i)
Some useful formulas maybe,
''If you have two places on the same latitude of 24° N, and the angle subtended between them is 120°,(circumference of earth is 40000km)
The shortest distance can be found as follows.
First find circumference of the parallel of latitude which is c=C*cos(theta)
So: c=*cos24° *40000km =36560km.
SO length of the arc PQ is : l=c*(a/360)
so: l=36560*120/360= 12186.7 km to 1DP.''
Hopefully this example and picture give some insight.
That is just an example. For part (ii) there is a similar way to calculate the latitude, but my book shows only examples where the longitude is the same... and in this case both the latitude and longitude are different.
Hi I've done a question on latitude and longitude.
It states : Take the radius of the earth to be 6400km and pi to be 3.142.
(i)The distance between Town P (63° N, 70°E) and Town R (63° N, x° E) is 900km.
If Town R is east of Town P, determine x°E, the longitude of R, to one decimal place.
Now I've done this using this formula: let (c) be the circumference of the parallel of latitude, and (C) be the circumference of the earth.
So I know that c = C*cos(theta)
C is = 40217.6km
And the length of the arc of latitude QY is : l=c*(a/360)
so : 900km=40217.6km *cos63° *a/360
a= (900*360)/(40217.6*cos63°)
a= 17.7
So I would have thought that now all I had to do was subtract this from the angle of longitude I have 70° but apparently its when I add 17.7° to 70° I get x = 87.7° which is the answer, this I don't understand as all the other examples in my book subtract.
Now for the second part of the question, this I'm stuck like Ive never been before.
''The shortest distance between Town P (63° N,70° E) and Town Q (y° N, 110° W) is 6702.9km
Determine y° N, the latitude of Q. (The answer is 57° if this helps anyone) I have no clue how to do this.
Here is a picture attached of how I got part (i)
Some useful formulas maybe,
''If you have two places on the same latitude of 24° N, and the angle subtended between them is 120°,(circumference of earth is 40000km)
The shortest distance can be found as follows.
First find circumference of the parallel of latitude which is c=C*cos(theta)
So: c=*cos24° *40000km =36560km.
SO length of the arc PQ is : l=c*(a/360)
so: l=36560*120/360= 12186.7 km to 1DP.''
Hopefully this example and picture give some insight.
That is just an example. For part (ii) there is a similar way to calculate the latitude, but my book shows only examples where the longitude is the same... and in this case both the latitude and longitude are different.
Last edited: