A ladder rests against a vertical wall at an inclination of 60 degrees to the horizontal. Its foot is pulled away from the wall through a distance "p"m so that the upper end slides down a distance of "q" m along the wall and then the ladder makes an angle 45 degrees to the horizontal. Find the value of p/q.

Dear Student,
Here is the solution of your asked query:
The given information can be represented diagrammatically as
 
 In the above figure AB and CD represent the same ladder
So, their length must be equal
Let length of the ladder be h
∴ AB = CD = h
Here, α=60° and β=45°In AEB;AEAB=sinα=sin60°=32AE=h32and BEAB=cosα=cos60°=12BE=h2Now, In DEC;DECD=sinβ=sin45°=12DE=h2and CECD=cosβ=cos45°=12CE=h2Now, pq=BCAD               =CE-BEAE-DE               =h2-h2h32-h2               =h2-h2h3-h22             =h2-hh3-h2 =2-13-2

Regards
 

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