# Science / Geography

posted by .

1. Begin journey at 40 degrees N by 77 degrees W.

2. Travel 4200 miles with a compass bearing of 130 degrees.

3. Travel 2800 miles with a compass bearing of 180 degrees.

4. Travel 5250 miles with a compass bearing of 90 degrees.

5. Travel 1750 miles with a compass bearing of 0 degrees.

6. Where is your location using latitude and longitude coordinates?

1 degree latitude = 70 miles

I know how to do this, however, your 1 degree latitude is just wrong. It could be that at some latitude, say the starting point, however, as soon as you go N or S it changes. Steps 3, and 5 is a considerable change in latitude, so the 1 degree = fixed value is wrong.
As one goes N or S, the conversion of miles to latitude difference changes. So even in step1, and step 4, it has to be considered. In step 4, you are not at the starting point anymore.

So how does one work this? The easy way is to plot it on a globe. The wrong way to work it is to plot it on a mercator projection (flat map).
The complicated way to solve it is to use spherical trignometry, which I doubt you have been introduced to.
http://star-www.st-and.ac.uk/~fv/webnotes/chapter2.htm
As you can see, the problem is that as the problem states the travel as straight paths, the real path traveled in each step was a curve on the surface of the Earth, not a straight line. Any attempt to measure it as a straight line is wrong. When the distances are large, as in this problem, the error is very large.
Plot this on a globe.

A reminder: Due to the curvature, step one 4200miles at a compass bearing 130 will make a spiral upwards as it is drawn on a sphere. You will have to be careful drawing the line segments to make it a constant angle with Longitude lines.
Wouldn't life be simple if you could use a flat map and ignore the fact that it is totally a wrong representation of Earth's surface?

## Similar Questions

1. ### Maths

The bearing of A from B is 060 degrees. What is the bearing of B from A?
2. ### Maths

What are bearings? Bearings are things that surround rotating shafts to reduce friction and wear. The word "bearing", as in compass bearing, can also refer to the direction that something is moving (such as 10 degrees east of north).
3. ### C Programming

How do you reprompt after the user inputs a wrong number into the program in C Programming?
4. ### calculus

A plane flies 810 miles from A to B with a bearing of 75 degrees. Then it flies 648 miles from B to C with a bearing of 32 degrees. Find the straightline distance from and bearing from C to A.
5. ### Math C30

An airplane is leaving the first airport (A) at a bearing of 70 degrees. It then travels 238 miles to airport B. After fueling up, it leaves at a bearing of 120 degrees and lands at airport C. After fueling up it finally returns to …
6. ### Math

A fishing boat leaves port at 11 miles per hour at a bearing of 210 degrees for 2 hours, then turns to a bearing of 250 degrees at 8 miles per hour for 4 hours, and finally changes to a bearing of 280 degrees at 7 miles per hour for …
7. ### math

A fishing boat leaves port at 11 miles per hour at a bearing of 210 degrees for 2 hours, then turns to a bearing of 250 degrees at 8 miles per hour for 4 hours, and finally changes to a bearing of 280 degrees at 7 miles per hour for …
8. ### Math

Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided …
9. ### Math

Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided …
10. ### Math(DifferentQuestion,SameDescription)

Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided …

More Similar Questions