moving ladder problem

[Thor66601]

I'm stuck!

A 10' ladder is against the wall. The angle between the top of the ladder and the wall is theta. The distance from the bottom of the ladder to the wall is X. The ladder slides away from the wall. How fast does X change with respect to theta when theta = Pi/3?

I started using the law of Sine to relate theta to X: sin (theta) = X/10

Do I differentiate w.r.t X now?

 

[daon2]

I'm stuck!

A 10' ladder is against the wall. The angle between the top of the ladder and the wall is theta. The distance from the bottom of the ladder to the wall is X. The ladder slides away from the wall. How fast does X change with respect to theta when theta = Pi/3?

I started using the law of Sine to relate theta to X: sin (theta) = X/10

Do I differentiate w.r.t X now?

That is the definition of sine, not the law of sines.

You have \(\displaystyle x = 10\sin\theta\). You want to find \(\displaystyle \dfrac{dx}{d\theta}\) at \(\displaystyle \theta=\pi/3\). So take the derivative w.r.t \(\displaystyle \theta\), and plug in your value!

 

[Thor66601]

That is the definition of sine, not the law of sines.

You have \(\displaystyle x = 10\sin\theta\). You want to find \(\displaystyle \dfrac{dx}{d\theta}\) at \(\displaystyle \theta=\pi/3\). So take the derivative w.r.t \(\displaystyle \theta\), and plug in your value!

Thank you - not sure why I was so determined to derive w.r.t X - this makes sense to me. Thank you again!