Angle of separation?

Question

You are at 37deg 49min 11sec S: 144deg 57min 3sec E

What is the angle of separation between

A 37deg 23min 55sec S : 144deg 34min 9sec E AND
B 37deg 20min 17sec S : 144deg 12min 59sec E

or better still - tell me how I can go about calculating it myself

Answer 1

These points are close enough together that you don't need spherical trig. you can assume the Earth is flat and use Pythagoras. We'll use secs as our units. 1 second=1/60 nautical mile. Call it 1. Draw a right angled triangle, sides 916 and 1270 at right angles. These are the differences in seconds between the lat and long of the two points. Next, multiply 1270, the longitudinal difference by 0.83 to get 1058 because a degree of longitude is 60NM times the cos of the latitude. Now we've got a right angled triangle, sides 916 and 1058 at right angles. Use Pythagoras to get hypotenuse = SQR (839056+1119364)= 1399.4 seconds.
Divide this by 60 to get 23.3 nautical miles.

Answer 2

A 37deg 23min 55sec S : 144deg 34min 9sec E AND
B 37deg 20min 17sec S : 144deg 12min 59sec E

To solve it, you can convert to decimal degrees with a calculator and find the difference, and then convert back to D m s.

Or you have to do it long hand. I can't show you, since your angles are ambiguous. A bearing, since you give one direction, needs TWO directions, like N 15 deg E, or S 25 deg W.

Azimuths, on the other hand are simple angles, rotated clockwise from North.

The basic way to do it longhand is to tabulate the dimensions with common directions, because a N E bearing and SW bearing can't simply be subtracted. Once you tabulate the angles, you start at the seconds position, and if the greater angle's second is less that the other, you subtract a minute and add 60 seconds then find the difference. You repeat with the minutes. If needed subtract a degree and add 60 minutes.

Find a surveying book which will illustrate this, or maybe there is an online example.