Question

A 15 m long ladder is placed against a wall in such a way that the foot of the ladder is a 9m away from the wall. Up to what height does the ladder reach the wall.

Answer 1

I hope it will help you

Answer 2

$Length \: of \:the \: ladder (AC) = 15 \: m$

$Distance \: between \: foot \:of \: ladder \:to \\base \:of \: the \: wall (BC) = 9 \:m$

$Height \: of \:wall (AB) = \red {?}$

$In \:\triangle ABC , we \: have ,$

$\angle{ ABC } = 90\degree$

$\blue { (By \: Pythagoras \:Theorem :)}$

$\boxed { \pink { AC^{2} = AB^{2} + BC^{2}}}$

$\implies 15^{2} = AB^{2} + 9^{2}$

$\implies 15^{2} - 9^{2} = AB^{2}$

$\implies 225 - 81 = AB^{2}$

$\implies 144 = AB^{2}$

$\implies \sqrt{144} = AB$

$\implies \sqrt{12^{2}}= AB$

$\implies AB = 12 \:cm$

Therefore.,

$\red {Height \: of \:wall}\green {= 12 \:cm}$

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