# Derivatives and rate of change

1. Nov 3, 2013

### physics604

1. A ladder 10 ft long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the
bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ=$\frac{∏}{3}$?

2. Relevant equations

The derivative rules.

3. The attempt at a solution

Using trig, I know the base of the triangle = 10sinθ)^2.

Using the Pythagorean Theorem, I get the equation

x^2=100-100sin^2θ

x=√100(1-sin^2θ)

What is my next step?

2. Nov 3, 2013

### dipole

Well, firstly you have your sines and cosines mixed up, the expression for $x$ should be,

$x = 10\sin\theta$.

Now that you have a functional relation between $x$ and $\theta$, what would the derivative of $x$ tell you?

3. Nov 3, 2013

### physics604

Ok I got it! I just drew my diagram wrong :P