at what rate is the angle shown changing at that instant? x=8 y=6 z=10

Question

dx/dt=-15 dy/dt=10 dz/dt=-6

so i tried it by doing
sin(0)=y/z
(d0/dt)cos(0)=(dy/dt)/(dz/dt)
(d0/dt)(8/10)=(-10/6)
(d0/dt)=-25/12 rad/hour
did i miss it because i didn't do the quotent rule?

Answer 1

It appears so. y and z are functions of t, so you need the quotient rule.

Answer 2

Ty