**Exercise:**

Alderney, in the Channel
Islands, has longitude 2°W, latitude 50°N.

Winnipeg, in
Canada, has longitude 97°W, latitude 50°N.

How far apart
are they, in nautical miles, along a great circle arc?

Use
the cosine rule:

cos AW = cos WP cos AP + sin WP sin AP cos P

=
cos^{2}40° + sin^{2}40° cos 95°

= 0.5508

So AW = 56.58°

=
3395
nautical miles

(This is 7% shorter than the route along a
parallel of latitude).

If you set off from Alderney on
a great-circle route to Winnipeg,

in what direction (towards what
azimuth) would you head?

Use the sine rule:

sin A /
sin WP = sin P / sin WA

so sin x = sin 40° sin 95° / sin
56.58° = 0.77

so x = 50.1° or 129.9° .

Common sense says 50.1° (or
check using cosine rule to get PW).

Azimuth is measured
clockwise from north,

so azimuth is 360° - 50.1° = 309.9°

(Note that this is 40° north of the “obvious” due-west course.)

Back to "Spherical trigonometry".