Related Rates - Angle rate
I'm not sure weather this is correct or not, but I gave it my best shot and it looks correct... but I'm not sure if it is.
So here is my try:
A 10 ft plank is leaning against a wall. If at a certain instant the bottom of the plank is 2 ft from the wall and is pushed toward the wall at a rate of 6 in/sec, how fast is the acute angle that the plank makes with ground increasing?
cos(theta) = 2/10 = 2/10
-sin(theta) d(theta)/dt = 2/10 dx/dt
-sin(theta) d(theta)/dt = 2/10 * .5ft/sec
-sin(theta) d(theta)/dt = 1/10
d(theta)/dt = 1/10 / -sin(theta)
d(theta)/dt = (1/10) / (sqrt(96) / 10)
d(theta)/dt = 1/sqrt(96) <---- answer?
I'm not sure weather or not to convert inches to feet. But when I don't convert then I get 12/sqrt(96) as my answer. :| Am I on the right track here?