For a right angled isosceles triangle of short sides 10km the
usual flat Pythagoras theorem gives a hypotenuse of
Using the Pythagoras on a sphere we have the length of the
hypotenuse equal to
The percentage error in this case is 0.00002%.
For the last part of the problem we have the following
results.
| x (km) |
Curved BC |
Flat BC |
Actual error |
% error |
| 10 |
14.14213 |
14.14214 |
0.000003 |
0.00002% |
| 100 |
141.418 |
141.421 |
0.003 |
0.002% |
| 200 |
282.82 |
282.84 |
0.03 |
0.009% |
| 300 |
424.2 |
424.3 |
0.1 |
0.02% |
| 400 |
565.5 |
565.7 |
0.2 |
0.04% |
| 500 |
706.7 |
707.1 |
0.4 |
0.06% |
| 656.2515676 |
927 |
928 |
0.9 |
0.1000000% |
| 1000 |
1411 |
1414 |
3.3 |
0.2% |
| 5000 |
6610 |
7071 |
461.3 |
7% |