A ladder rests against a wall at an angle α to the horizontal. When its foot ispulled away from the wall through a distance a, it slides a distance b down thewall and makes an angle β with the horizontal. Show that a/b = (cosα - cosβ)/(sinα - sinβ ).
Given:
Let the length of the ladder be l units.
In right angled Δ ACD,
sin β = DC / AB
= DC / l ,
Also
cos β = ( a + BC) / AB
= (a + BC) / l …………. (i)
In right angled Δ EBC,
sin α = (b + DC) / BE
= (b + DC) / l ,
cos α = BC / BE
= BC / l ………….(ii)
From (i) and (ii)
= (-a) / (-b)
= a / b
= L.H.S.
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