Derivatives and rate of change

[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}?

Homework Equations

The derivative rules.

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?

 

[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?

 

[physics604]

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