Question

Let θ (in radians) be an acute angle in a right triangle and let x and y, respectively, be the lengths of the sides adjacent to and opposite θ. Suppose also that x and y vary with time.
At a certain instant x=7 units and is increasing at 3 unit/s, while y=1 and is decreasing at 18 units/s.
How fast is θ changing at that instant?

Answer 1

The equation is supposedly
[cos^2(theta)/x^2]*[(x*dy/dt)-(y*dx/dt)]

Answer 2

you know that
tanθ = y/x
sec^2θ dθ/dt = (x dy/dt - y dx/dt)/x^2
so just plug in your numbers.

Answer 3

if that confuses you, just recall the quotient rule for derivatives, and implicit differentiation.