1. The path of a swing boat fairground ride that swings forwards and backwards is modelled as the arc of a circle, radius $8m$, as shown in the diagram below.

Ground level is represented by the $x$-axis.

The value of $x$ represents the horizontal displacement, in metres, of the swing boat relative to the origin.

The value of $y$ represents the height, in metres, of the swing boat above ground level.

The height of the swing boat is modelled using

$y=12-\sqrt{100-{x}^{2}},-8\leqx\leq8$

(i) Find the height of the boat when it’s horizontal displacement is 6 m.

(ii) Find the horizontal distance from the origin when the boat is $5$m above the ground, giving your answer to three significant figures.

(iii) Find the maximum height the swing boat reaches.

(iv) When at its maximum height, find the angle of elevation of the swing boat from the origin.