Answer:
θ is decreasing at the rate of  units/sec
 units/sec
or  (θ) =
(θ) = 
Step-by-step explanation:
Given :
Length of side opposite to angle θ is y
Length of side adjacent to angle θ is x
θ is part of a right angle triangle
At this instant,
x =  8 ,  = 7
 = 7 
(  denotes the rate of change of x with respect to time)
 denotes the rate of change of x with respect to time)
y = 8 ,  = -14
 = -14
( The negative sign denotes the decreasing rate of change )
Here because it is a right angle triangle,
tanθ =  -------------------------------------------------------------------1
-------------------------------------------------------------------1
At this instant,
tanθ =  = 1
 = 1
Therefore θ = π/4
We differentiate equation (1) with respect to time in order to obtain the rate of change of θ or  (θ)
(θ)
 (tanθ) =
 (tanθ) =  (y/x)
 (y/x) 
( Applying chain rule of differentiation for R.H.S as y*1/x)
 θ
θ (θ) =
(θ) = 
 -
 - 
 -----------------------2
-----------------------2
Substituting the values of x , y ,  ,
 ,  , θ at that instant in equation (2)
 , θ at that instant in equation (2)
2 (θ) =
(θ) =  *(-14)-
*(-14)-  *7
*7
 (θ) =
(θ) = 
Therefore θ is decreasing at the rate of  units/sec
 units/sec
or   (θ) =
(θ) = 