i need major help?

Question

In the right-angled triangle the angle theta is increasing at a constant rate of 6 radians per hour. At what rate is the side of length x increasing when x= 3 ft?

the pic they have is
http://i181.photobucket.com/albums/x85/ctti_3/untitled-19.jpg

Answer 1

sin(θ) = x/5

Implicitly differentiate:
(dθ/dt) cos(θ) = (1/5)(dx/dt)
6 * cos(θ) = (1/5) dx/dt

sin(θ) = 3/5
--> cos(θ) = 4/5 (Pythagorean theorem)

6*(4/5) = (1/5) dx/dt
120/5 = dx/dt
dx/dt = 24 ft/hr

Answer 2

see that the diagram is a 3-4-5 triangle
define x as x= 5 * sine theta
dtheta / dt = 6 radians/hr
dx/dt = 5*cos theta * dtheta/dt
= 5 * 4/5 *6 = 24 ft/hr