ok...here we go with the ladder! Related Rates. 24' ladder hanging over a 7' fence - what is the rate the top is decending to the ground when the base is 7' away from the fence. I think I am trying to cal the rate change of the triangle? This is not a simple scenario....help! Thanks

Question

ok...here we go with the ladder!  Related Rates.  24' ladder hanging over a 7' fence - what is the rate the top is decending to the ground when the base is 7' away from the fence.  I think I am trying to cal the rate change of the triangle?  This is not a simple scenario....help!  Thanks

anonymous · Answer

Looks like we need to use some implicit differentiation here.  So we know the length of the ladder, 24 feet, and it rests over a 7 foot wall, so the total height of the ladder against the wall would be y+7.  Using the pathagorean theorem, we have, 
$$24^2= x^2+(y+7)^2$$ We differentiate with respect to x and get, 
$$0=2x+2(y+7)dy/dx$$ We know the length of the ladder is not changing, so it's rate of change is zero.  Now you can solve for dy/dx and you will have the rate of change of the y position of the ladder when you sub in 7 for x.