A ladder makes an angle of $60^{\circ}$ $60^@$ 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 ${16.78}^{\circ}$ $16.78^@$

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

enter image source here

Therefore $\frac{h}{x} = {sin 60}^{\circ} = \frac{\sqrt{3}}{2}$ $h/x=sin60^@=sqrt3/2$

or $x = \frac{2 h}{\sqrt{3}}$ $x=(2h)/sqrt3$

Hence length of longer ladder is $3 \times \frac{2 h}{\sqrt{3}} = 2 \sqrt{3} h$ $3xx(2h)/sqrt3=2sqrt3h$

and $sin θ = \frac{h}{2 \sqrt{3} h} = \frac{1}{2 \sqrt{3}} = \frac{\sqrt{3}}{6} = 0.2887$ $sintheta=h/(2sqrt3h)=1/(2sqrt3)=sqrt3/6=0.2887$

and $θ = {sin}^{- 1} 0.2887 = {16.78}^{\circ}$ $theta=sin^(-1)0.2887=16.78^@$

Hence, longer ladder makes an angle of ${16.78}^{\circ}$ $16.78^@$

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?