# Thread: I am getting approximalte half what the answer should be (Related Rates Problem)

1. ## I am getting approximalte half what the answer should be (Related Rates Problem)

I am having trouble with this question but I believe it's a small mistake because I get approximately half of what the answer should be. I attached my work.

Question: "A ladder 10 ft long leans against a vertical wall. If the bottom of the ladder slides away from the base of the wall at a speed of 2 ft/s, how fast is the angle between the ladder and the wall changing when the bottom of the ladder is 6ft from the base of the wall?

Any help would be greatly appreciated!

2. Originally Posted by s3a
I am having trouble with this question but I believe it's a small mistake because I get approximately half of what the answer should be. I attached my work.

Question: "A ladder 10 ft long leans against a vertical wall. If the bottom of the ladder slides away from the base of the wall at a speed of 2 ft/s, how fast is the angle between the ladder and the wall changing when the bottom of the ladder is 6ft from the base of the wall?

Any help would be greatly appreciated!
let $\displaystyle \theta$ = angle between the ladder and the wall

$\displaystyle \sin{\theta} = \frac{x}{10}$

$\displaystyle \cos{\theta} \cdot \frac{d\theta}{dt} = \frac{1}{10} \cdot \frac{dx}{dt}$

$\displaystyle \frac{8}{10} \cdot \frac{d\theta}{dt} = \frac{2}{10}$

$\displaystyle \frac{d\theta}{dt} = \frac{2}{10} \cdot \frac{10}{8} = \frac{1}{4}$ rad/s

3. So my mistake was that SINE is what determines "THE ANGLE BETWEEN THE LADDER AND THE WALL?" Also, I now see the ladder is a constant and the x is not. Thanks.

4. Originally Posted by s3a
So my mistake was that SINE is what determines "THE ANGLE BETWEEN THE LADDER AND THE WALL?"
I don't know ... I don't do downloads on public message forums anymore.

5. Oh, well thanks still but if you didn't know, choosing to open rather than save pdf files would just store them into the hard drive temporarily.