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  • A foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground.if the ladder is shifted in such a way that its feet is 8m away from the wall,to what height does its top reaches

A foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground.if the ladder is shifted in such a way that its feet is 8m away from the wall,to what height does its top reaches

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\\ \text{The 'ladder', 'height to which it reaches' and 'foot of ladder from wall' forms a} \\ \text{ right angled triangle. ladder} \\ \text{ = hypotenuse(h) height to which it reaches = base(b) foot of ladder from wall = altitude(a)} \\ \ initially,\ a =8 m , b =6 m$ \\ $h^{2}=a^{2}+b^{2}$ \\ $\left.\left.\Rightarrow h =\sqrt{(} a ^{2}+ b ^{2}\right)=\sqrt{(} 8^{2}+6^{2}\right)=\sqrt{100} =10 m$ when foot is $8 m$ away from wall, \\ $b =8 m , h =10 m , a =?$ \\$h^{2}=a^{2}+b^{2}$ \\$\Rightarrow a ^{2}= h ^{2}- b ^{2}$ \\$\left.\left.\Rightarrow a=\sqrt{(} h^{2}-b^{2}\right)=\sqrt{(} 10^{2}-8^{2}\right)=\sqrt{3} 6=6 m$ \\So its top reaches $6 m$ height

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Deependra Verma

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