Question

A ladder makes an angle of `60^@` to a pole. What angle would be made by a ladder, which is three times longer than this ladder, on a pole of same height?

Answer 1

Longer ladder makes an angle of `16.78^@`

Explanation:

Let the longer ladder whose length is say `x` make an angle of `theta`. The picture appears as one given below.

Therefore `h/x=sin60^@=sqrt3/2`

or `x=(2h)/sqrt3`

Hence length of longer ladder is `3xx(2h)/sqrt3=2sqrt3h`

and `sintheta=h/(2sqrt3h)=1/(2sqrt3)=sqrt3/6=0.2887`

and `theta=sin^(-1)0.2887=16.78^@`

Hence, longer ladder makes an angle of `16.78^@`