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Question Number 106373 by chichi last updated on 04/Aug/20

  A ladder placed against a vertical walls  ubtends an angle of 45 degree with   thewall The distance between the footo  f the ladder and the wall is 15mt  calculae the length of the ladder   correctto the nearest whole number.

$$ \\ $$$$\mathrm{A}\:\mathrm{ladder}\:\mathrm{placed}\:\mathrm{against}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{walls} \\ $$$$\mathrm{ubtends}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{45}\:\mathrm{degree}\:\mathrm{with}\: \\ $$$$\mathrm{thewall}\:\mathrm{The}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{footo} \\ $$$$\mathrm{f}\:\mathrm{the}\:\mathrm{ladder}\:\mathrm{and}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{is}\:\mathrm{15mt} \\ $$$$\mathrm{calculae}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ladder}\: \\ $$$$\mathrm{correctto}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{whole}\:\mathrm{number}. \\ $$

Answered by 1549442205PVT last updated on 05/Aug/20

The length of ladder is ((15)/(cos45°))=((15)/((√2)/2))  =((30)/(√2))=15(√2)≈21 m

$$\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:\mathrm{ladder}\:\mathrm{is}\:\frac{\mathrm{15}}{\mathrm{cos45}°}=\frac{\mathrm{15}}{\sqrt{\mathrm{2}}/\mathrm{2}} \\ $$$$=\frac{\mathrm{30}}{\sqrt{\mathrm{2}}}=\mathrm{15}\sqrt{\mathrm{2}}\approx\mathrm{21}\:\mathrm{m} \\ $$

Commented by chichi last updated on 05/Aug/20

  thanks a lot for your help

$$ \\ $$$$\mathrm{thanks}\:\mathrm{a}\:\mathrm{lot}\:\mathrm{for}\:\mathrm{your}\:\mathrm{help} \\ $$

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