How does the height of a leaning ladder change with respect to its angle?

[karush]

A 10ft ladder leans against a wall at angle $\theta$ with the horizontal. The top of the ladder is $x$ ft above the ground.
If the bottom of the ladder is pushed toward toward the wall, find the rate at which x changes with respect to $\theta$ when $\theta = 60^0$. Express the answer in units of feet\degree

Well this is not related to time. And I thot that using $\sin{\theta}=\frac{x}{10}$ but after taking derivatives I couldn't get the Answer of 0.087 ft / degree.

 

[MarkFL]

Did you account for the conversion from ft/rad to ft/deg? Doing so will give you the answer you cite. :D

 

[karush]

Well. I did this

$10\sin{\theta}=x$

$\frac{d}{d\theta}10\cos{\theta}=\frac{d}{dx}$

 

[MarkFL]

This is what I did:

$$\sin(\theta)=\frac{x}{10}$$

Implicitly differentiate with respect to $\theta$:

$$\cos(\theta)=\frac{1}{10}\cdot\d{x}{\theta}$$

$$\left.\d{x}{\theta}\right|_{\theta=\frac{\pi}{3}}=10\cos\left(\frac{\pi}{3}\right)\frac{\text{ft}}{\text{rad}}=5\frac{\text{ft}}{\text{rad}}\cdot\frac{\pi\text{ rad}}{180\text{ deg}}=\frac{\pi}{36}\,\frac{\text{ft}}{\text{deg}}$$

 

[karush]

OK, see now, I didn't know how to deal with the radiansSo $$\frac{\pi}{36}=0.087$$'

 

[karush]

The best answer and method was here at MHB

I went to some other sites with this problem but the method was hard to understand plus the answer was wrong. I should just stay here.