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?

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Answer 1 · 2017-04-05T05:41:28

Longer ladder makes an angle of $16.78^@$

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

enter image source here

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 $16.78^@$

A ladder makes an angle of 60^@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?