Answer: [tex]9\ ft/rad[/tex]
Step-by-step explanation:
Given
Length of the ladder is [tex]l=18\ ft[/tex]
Angle between the wall and the ladder is [tex]\theta[/tex]
from the figure, we can write
[tex]\Rightarrow \sin \theta=\dfrac{x}{18}\\\\\Rightarrow x=18\sin \theta[/tex]
Differentiate the above equation w.r.t [tex]\theta[/tex]
[tex]\Rightarrow \dfrac{dx}{d\theta}=18\cos \theta\\\\\text{at }\theta=\dfrac{\pi }{3}\\\\\Rightarrow \dfrac{dx}{d\theta}=18\cos(\dfrac{\pi}{3})\\\\\Rightarrow \dfrac{dx}{d\theta}=18\times 0.5\\\\\Rightarrow \dfrac{dx}{d\theta}=9\ ft/rad[/tex]
