Question

A ladder 18 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=π/3?
x′(π/3)=

Answer 1

\[12\cos \theta \]

Answer 2

x = 18sin(t)
x' = 18cos(t)
x'(pi/3) = 18cos(pi/3) = 9

Answer 3

thanks that makes sense