Let us consider the Cartesian co-ordinates of the point are \( (x,\ y,\ z) \),

Given, the spherical polar co-ordinates of that point are

\( r=16 \)

\( \theta=60^{\circ} \)

\( \phi=30^{\circ} \)

We know that,

\( x=r\ \sin\theta\ \cos\phi= 16\times\sin{60^{\circ}}\times\cos{30^{\circ}} \)

\( or,\ x=16\times\frac{\sqrt{3}}{2}\times\frac{\sqrt{3}}{2}=12 \)

\( y=r\ \sin\theta\ \sin\phi=16\times\sin{60^{\circ}}\times\sin{30^{\circ}} \)

\( or,\ y=16\times\frac{\sqrt{3}}{2}\times\frac{1}{2}=4\sqrt{3} \)

And,

\( z=r\ \cos\theta=16\times\cos{60^{\circ}} \)

\( or,\ z=16\times\frac{1}{2}=8 \)

So the cartesian co-ordinates of the point are \( (12,\ 4\sqrt{3},\ 8) \)

[ To know the relation between three-dimensional cartesian co-ordinates and the spherical polar co-ordinates (CLICK HERE) ]