A 15 foot ladder is leaning against a building. The base of the ladder begins to slide away from the wall at a rate of 2.5 ft/s

Question

anonymous · Answer

b) at what rate is the angle formed by the ladder and the floor decreasing when the base of the ladder is 10 ft from the wall?

anonymous · Answer

pythag for this one
$$x^26y^2=15^2\2xx'+2yy'=0$$ or 
$$xx'+yy'=0$$

anonymous · Answer

oops now we are in to trig

anonymous · Answer

i have no idea how to start it off...

anonymous · Answer

draw
use tangent

anonymous · Answer

or sine maybe

anonymous · Answer

or cosine

anonymous · Answer

|dw:1430273535063:dw|

anonymous · Answer

$$\cos(\theta)=\frac{x}{15}$$

anonymous · Answer

isnt x 10 though?

anonymous · Answer

x is a variable

anonymous · Answer

you are looking for the rate of change of $\theta$ right?

anonymous · Answer

yes

anonymous · Answer

start with 
$$\huge \cos(\theta)=\frac{x}{15}$$ sp 
$$\huge -\sin(\theta)\theta'=\frac{x'}{15}$$ by the chain rule

anonymous · Answer

ok so thats exaclty where im confused where did sine come from

anonymous · Answer

it is minus sine

anonymous · Answer

on account of that is the derivative of cosine right?

anonymous · Answer

it is? i haven't done derivatives with trig yet so.....     highschool calculus if your wondering

anonymous · Answer

you cannot do this without trig 
no way, no how

anonymous · Answer

oh okay so maybe i didnt have to do this part of the question then... since i havent learned how to derive trig yet