Question

the angle of elevation of a ladder leaning against a wall is 60degrees and the foot of the length of ladder is 4.6 m away from the wall .the length of the ladder is​

Answer 1

$From \:the \: figure \:above ,$

$In \: \triangle ABC ,$

$Distance \:from \:base \:of \:the \: wall \:to$

$foot \:of \:the \: ladder ( BC) = 4.6 \:m$

$Angle \:of \: elevation \: a \: ladder \: leaning$

$a \:wall \: is \: 60\degree$

$Cos 60\degree = \frac{CB}{AC}$

$Let \: length \:of \: the \: ladder = AC$

$\implies \frac{1}{2} = \frac{4.6}{AC}$

$\implies AC = 4.6 \times 2$

$\implies AC = 9.2 \:m$

Therefore.,

$\red{Length \:of \: the \: ladder} \green{=9.2 \:m}$

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Answer 2

$\bf{\underline{\underline{\bigstar\bigstar\: Figure : }}}$

$\:\:$

$\setlength{\unitlength}{1.6mm}\thickline\put(5.8,0){\line(-1,1){25}}\put(-19,0){\line(1,0){25}}\put(-19,0){\line(0,1){25}}\qbezier(0,5.5)(-4,3)(0,0)\put(-9,-2){4.6m}\put(-5,2){{60}^{\circ}}\put(-7,15){hypotenuse}\put(-24,15){height}\put(-17.5,-2){\huge{\square}}$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar Given : }}}$

$\:\:$

• $\footnotesize{ Angle \: of \: elevation = {60}^{\circ} }$

• $\footnotesize{ Distance \: between \: foot \: of \: ladder \: from \: wall(Base) = 4.6m }$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\: To \: Find : }}}$

$\:\:$

• $\footnotesize{ Length \: of \: ladder(hypotenuse) }$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\: Solution :}}}$

$\:\:$

$\footnotesize{ Cos\theta = \dfrac{base}{hypotenuse} }$

$\footnotesize{\implies Cos{60}^{\circ} = \dfrac{4.6m}{hypotenuse} }$

$\footnotesize{\implies \dfrac{1}{2} = \dfrac{4.6m}{hypotenuse} }$

$\footnotesize{\implies hypotenuse = 4.6m \times 2 }$

$\footnotesize{\implies hypotenuse = 9.2m }$

$\:\:$

$\bold{ Length \: of \: ladder(hypotenuse) = 9.2m }$