Let θ be the angle between the floor and the ladder.
cosθ=x5
⇒−sinθdθdt=15×dxdt...(1)
Given dxdt=0.5m/sec .......(2)
Also sinθ=y5
Given that the ladder is 3 m away from the wall.
As per pythagoras theorem, when the ladder of length 5 m is 3 m away from the wall then y=4 m
Therefore when y=4,sinθ=45 .......(3)
Substitue (2) and (3) in (1) we get
−45dθdt=15×0.5
dθdt=−0.54=−18 rad/sec
Negative sign indicates that θ is decreasing