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A ladder rests against a wall at an angle a to the horizontal. Its foot is pulled away from the B wall through a distance p, so that it slides a distance q down the wall making an angle β with the horizontal. Prove that : p/q = (cosβ - cosα)/(sinα - sinβ)
 

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Let AB is a wall and AC is a ladder with length x.

The foot of ladder is pulled through distance p so that it slides a distance q down the wall.

∠ACB = α and ∠EDB = β

From right angled ∆ABC,

sin α = AB/AC

⇒ sin α = AB/x

⇒ AB = x sin α …..(i)

and cos α = BC/AC

⇒ cos α = BC/x

⇒ BC = x cos α ….(ii)

BD = BC + CD

= x cos α + p

BE = AB – AE

= x sin α – q ….(iii)

From right angled ∆EBD,

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