Answer to Question #136346 in Trigonometry for noel ludovice

Question

Explain why the polar distance of a great circle is exactly 90°? _______________________________________________________

Answer 1

A great circle is the largest possible circle that can be drawn around a sphere. All spheres have great circles.

The equator is an example of a great circle: one whose plane passes through the centre of the sphere.

Every great circle has two poles. We can define these:

     (a) as the points which are 90° away from the circle, on the surface of the sphere.

     (b) as the points where the perpendicular to the plane of the great circle cuts the surface of the sphere.

These two definitions are equivalent.

The length of a great-circle arc on the surface of a sphere

is the angle between its end-points, as seen at the centre of the sphere,

and is expressed in degrees (not miles, kilometres etc.).

A great circle is a geodesic (the shortest distance between two points) on the surface of a sphere,

analogous to a straight line on a plane surface.

So as we cut a great circle into two it equally divides into two half parts so it has two poles and which are perpendicular to each other that is why the polar distance of a great circle has exactly 90^° of angle.