What exactly does arc sin mean? If 'a rough plane is inclined at arc sin 7/25 to the horizontal' does this mean that the opposite vector to the angle is 7 and the hypotenuse is 25?
It is the inverse of sin. Sometimes written as sin-1. So as sin = opp/hyp, the sin of the angle is 7/25, i.e Sin(A) = 7/25. The arc sin of 7/25 will get you the answer A,(approx 16 deg.) The opposite and hypotenuse doesn't necessarily = 7 and 25, it could be any multiple, i.e. 14 and 50, etc.
...just to add, we're not necessarilly talking triangles here, the hypotenuse and plane could go on infinately, but if you drop a perpendicular (to the plane) from any point on the hypotenuse, the ratio will always be the same, i.e. 7/25, where 7 is the opp, and 25 is the hyp.