Question

A ladder rests against a vertical wall at an inclination alpha to the horizontal. Its foot is pulled away from the wall through a distance p so that its upper end slides distance q down the wall and then the ladder makes an angle beta to the horizontal.

Answer 1

Answer:

let

BC= H

AC= L m

DE= L m

AD= p m

AB= x

EC= q

in triangle ABC

sin alpha=BC/AC = H/L

cos alpha=AB/AC = x/L

in triangle EBD

sin beta=BE/DE

BC-EC/DE

=H-q/L........1

cos beta=AB+DA/DE

p+x/L.........2

rhs= cos beta–cos alpha/sin alpha–sin beta

p+x/L–x/L=(cos beta–cos alpha)

p+x–x/L.......3

H/L–H–q/L=(sin alpha–sin beta)

H–(H–q)/L......4

from eq 3 and 4

L and L get cancelled

so we get

=p+x–x/H–(H–q)

=p/q

so LHS=RHS