Help me, Mathletes!

[morkus64]

Trying to find the angle between Cleveland (41° 29' N / 81° 41' W) and Jerusalem (31° 47'N 35° 10'E).

Thanks!

 

[purbeast0]

that makes absolutely no sense... there is no angle on a line.

EDIT: err i guess it could be 180 degrees heh.

 

[rcpratt]

that makes absolutely no sense... there is no angle on a line.

I assume he wants the angle relative to a latitudinal line.

 

[coxmaster]

Are you asking for a heading? Aka, the magnetic direction you would have to fly?

 

[Train]

that makes absolutely no sense... there is no angle on a line.

typically a question like this means an angle against a fixed line, in this case the equator makes perfect sense. Since latitude and longitude exist in a coordinate system, an axis in the system is considered a reference point. Similar to how someone says "angle of elevation", it is implied that the ground is the baseline of 0 degs.

Start with this premise: "The angle between two locations on the equator is 0 degrees"

 

[purbeast0]

I assume he wants the angle relative to a latitudinal line.

typically a question like this means an angle against a fixed line, in this case the equator makes perfect sense. Since latitude and longitude exist in a coordinate system, an axis in the system is considered a reference point.

Start with this premise: "The angle between two locations on the equator is 0 degrees"

heh, the ambiguity is shown 4 posts deep!

 

[darkxshade]

The answer is 42... thanks for playing

 

[preCRT]

Do your own homework.

 

[rcpratt]

The distance between Cleveland and Jerusalem is 9.70 degrees south and 116.85 degrees east according to your numbers.

So...tan(theta)=9.70/116.85, theta = -4.73457 degrees?

 

[morkus64]

typically a question like this means an angle against a fixed line, in this case the equator makes perfect sense. Since latitude and longitude exist in a coordinate system, an axis in the system is considered a reference point. Similar to how someone says "angle of elevation", it is implied that the ground is the baseline of 0 degs.

Start with this premise: "The angle between two locations on the equator is 0 degrees"

Thank you Train - that is what I mean.

 

[Train]

The distance between Cleveland and Jerusalem is 9.70 degrees south and 116.85 degrees east according to your numbers.

So...tan(theta)=9.70/116.85, theta = -4.73457 degrees?

The problem is the latitude/longitude system isnt equivlant to a cartesian coordinate system, longitudinal lines vary in distance from eachother at every latitude. The actual calculation of angles on the surface of the earth is a PITA function. I've used it before, but I'm too lazy to look it up now..

 

[rcpratt]

The problem is the latitude/longitude system isnt equivlant to a cartesian coordinate system, longitudinal lines vary in distance from eachother at every latitude. The actual calculation of angles on the surface of the earth is a PITA function. I've used it before, but I'm too lazy to look it up now..

Mmm, true enough. Yeah, I'm not going to carry it any further than that.

However, due to the relatively small longitudinal change, I'd expect it to be pretty close.

 

[morkus64]

The problem is the latitude/longitude system isnt equivlant to a cartesian coordinate system, longitudinal lines vary in distance from eachother at every latitude. The actual calculation of angles on the surface of the earth is a PITA function. I've used it before, but I'm too lazy to look it up now..

I thought there was something weird like that going on. It's beyond me - anyone care to prove their math prowess?

 

[Train]

I thought there was something weird like that going on. It's beyond me - anyone care to prove their math prowess?

Google "Great Circle Function" or maybe it's "Great Arc function" this is the function to determine the distance between two points in a polar coordinate system, perhaps that will lead you to a solution to find angles.

 

[morkus64]

Gah. I can't figure it out. Everything I try gives me stuff about the distance between two points on the earth, or I just can't understand what I'm looking at. Even Wolfram Alpha just shrugged at me.

 

[morkus64]

Ok, I think I got it, thanks to

http://web.archive.org/web/20060630011442/http://www.kcatv.org/calc.htm

It just seems strange that it would be at around 40 degrees north of east.

 

[rcpratt]

Ok, I think I got it, thanks to

http://web.archive.org/web/20060630011442/http://www.kcatv.org/calc.htm

It just seems strange that it would be at around 40 degrees north of east.

That seems incredibly wrong.

 

[morkus64]

That seems incredibly wrong.

It does, but it makes sense when you think about latitude and longitude lines not actually making a grid - the distance between longitudinal lines get larger the closer you get to the equator, so it would make sense that an arc cutting through the shortest distance would tend toward the poles. I think.

 

[Train]

Trying to find the angle between Cleveland (41° 29' N / 81° 41' W) and Jerusalem (31° 47'N 35° 10'E).

Thanks!

here's an idea to double check your answer.

Create a right triangle using the points. Add a 3rd point straight south of cleveland, and straight west of jerusalem. Now use the distance functions to get the lengths of all sides, and use trig to get the angle.

Though now that I think of it, because the triangle is on a sphere and not a flat surface, it may not be accurate still. But worth a shot to get another answer.

 

[rcpratt]

It does, but it makes sense when you think about latitude and longitude lines not actually making a grid - the distance between longitudinal lines get larger the closer you get to the equator, so it would make sense that an arc cutting through the shortest distance would tend toward the poles. I think.

Yeah, now that I think about it it does make sense. Since they are separated by nearly a third of the globe, heading towards the pole would make more sense.

And yeah Train, the trig thing isn't going to work for the same reason the trig I tried earlier won't.

 

[GoSharks]

nm

 

[krylon]

This thread is now about pie

and how I'm going to stick my junk all up in it

 

[Printer Bandit]

9000°

 

[Fenixgoon]

here's what you need:
1x transparency sheet
1x wulff net
1x sharpie/dry erase marker

put the transparency over the wulff net. draw the appropriate points of latitude and longitude on the transparency.

now, place both points along the equator line of the wulff net. the distance between the two points along the equator will be equivalent to the angle between them.