Trig question

 x=acos(1 - h /R)  means that

cosx = ( 1 - h/R)

And using the identity

1 - cos^2x = sin^2x , we have

1 - [ 1 - 2h/R + h^2/R^2]  = sin^2x     simplify

[  2h/R - h^2/R^2]  = sin^2x       simplify and take the square root of each side [and assuming the sine is positive]

√[2hR/R^2 - h^2/R^2]  = sin x     

√ [ 2hR - h^2] / R  = sin x       multiply both sides by R

√ [ 2hR - h^2] /   = R sin x

You're a hero.

Thanks!