Find angle of latitude: distance between P (63° N, 70°E), R (63° N, x° E) is 900km

[Dr.Peterson]

Well right, one is positive and one is negative... so it tells me they're on the same circle perhaps?

In particular, 110 - (-70) = 180, which is why they are on the same "vertical" circle. Can you use that, with essentially the same technique as if the longitudes were the same, to solve the problem?

[richiesmasher]

In particular, 110 - (-70) = 180, which is why they are on the same "vertical" circle. Can you use that, with essentially the same technique as if the longitudes were the same, to solve the problem?

Hmm... I keep getting 59 degrees, perhaps I'm doing this wrong?
I'm actually unsure of the method I must use...

[Dr.Peterson]

Hmm... I keep getting 59 degrees, perhaps I'm doing this wrong?
I'm actually unsure of the method I must use...

You said that the answer is supposed to be 57°, but that is not correct. Nor is 59°.

Please show your work. How did you get 59? How did you convert the given distance to degrees of latitude?

[richiesmasher]

You said that the answer is supposed to be 57°, but that is not correct. Nor is 59°.

Please show your work. How did you get 59? How did you convert the given distance to degrees of latitude?

I did this, using the formula for length of an arc of latitude

l=C*(a)/360

so:6702.9= 40217.6*cos63*a/360

(a)= (6702.9*360)/(40217.6*cos63)

(a)= 59.9

[Dr.Peterson]

I did this, using the formula for length of an arc of latitude

l=C*(a)/360

so:6702.9= 40217.6*cos63*a/360

(a)= (6702.9*360)/(40217.6*cos63)

(a)= 59.9

I don't get 59.9 from that calculation; but I did get 59.9997 from the correct calculation. You didn't really want to use cos(63), did you? (That would be for longitude.)

Assuming you really did the correct calculation, your problem is just that you are not finished. That is the number of degrees AWAY from the given point, not its latitude!

[richiesmasher]

I don't get 59.9 from that calculation; but I did get 59.9997 from the correct calculation. You didn't really want to use cos(63), did you? (That would be for longitude.)

Assuming you really did the correct calculation, your problem is just that you are not finished. That is the number of degrees AWAY from the given point, not its latitude!

OK I did the formula for an arc of longitude instead,

l=C*(a)/360

6702.9=40217.6*(a)/360
(a) = (6702.9*360)/40217.6
(a) = 59.9997 degrees

Now I have to either add or subtract this value from 63 degrees, because it's the latitude that is given would be the sector angle no?

[Dr.Peterson]

OK I did the formula for an arc of longitude instead,

l=C*(a)/360

6702.9=40217.6*(a)/360
(a) = (6702.9*360)/40217.6
(a) = 59.9997 degrees

Now I have to either add or subtract this value from 63 degrees, because it's the latitude that is given would be the sector angle no?

Right. So do that! (You'll find that only one choice works, otherwise there could have been two answers.)

You WILL get the book's answer; I hadn't done the full problem on paper, and missed one step before. You may make the same mistake before you are finished!

[richiesmasher]

Right. So do that! (You'll find that only one choice works, otherwise there could have been two answers.)

You WILL get the book's answer; I hadn't done the full problem on paper, and missed one step before. You may make the same mistake before you are finished!

I got it, I have to add, because it's North, and I'd round 59.9997 to 60 degrees, then I will add it to 63 ang get 123, then subtract that from 180 giving 57 degrees.

Thanks for all the help Doctor Pete.

[Dr.Peterson]

I got it, I have to add, because it's North, and I'd round 59.9997 to 60 degrees, then I will add it to 63 and get 123, then subtract that from 180 giving 57 degrees.

Thanks for all the help Doctor Pete.

Perfect. Interesting problem, wasn't it?

[richiesmasher]

Perfect. Interesting problem, wasn't it?

Indeed it was