7 The points \(A ( 0,35,120 ) , B ( 28,21,120 )\) and \(C ( 96,35 , - 72 )\) lie on the sphere \(S\), with centre \(O\) and radius 125 . Triangle \(A B C\) is denoted by \(\triangle\).
- Find, in simplest surd form, the area of \(\Delta\).
The points \(A , B\) and \(C\) also form a spherical triangle, \(T\), on the surface of \(S\). Each 'side' of \(T\) is the shorter arc of the circle, centre \(O\) and radius 125, which passes through two of the given vertices of \(T\). In order to find an approximation to the area of the spherical triangle, \(T\) is being modelled by \(\Delta\).
- (a) State the assumption being made in using this model.
(b) Say, giving a reason, whether the model gives an under-estimate or an over-estimate of the area of \(T\).