Math, asked by shantelnyongesa, 8 months ago

The angle of elevation of a ladder leaning against a wall is 60 degrees and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is ___ m. Type your answer below

Answers

Answered by Cosmique
87

Given :

  • A ladder is leaning against a wall
  • angle of elevation of ladder = 60°
  • distance of foot of ladder from wall = 4.6 m

To find :

  • Length of ladder

Figure :

\setlength{\unitlength}{1cm}\begin{picture}(6,4)\thicklines\put(0,0){\line(1,0){4}}\put(0,0){\line(0,1){4}} \put(0,4){\line(1,-1){4}}\put(0,0.4){\line(1,0){0.4}}\put(0.4,0){\line(0,1){0.4}}\qbezier(3.2,0)(3,0.4)(3.5,0.5)\put(2.5,0.3){$60^{\circ}$}\put(-0.5,-0.5){A}\put(0,4.5){B}\put(4,-0.5){C}\put(1.5,-0.5){4.6\;m}\put(2.5,2.5){\bf{x}}\end{picture}

  • where AB is the wall
  • AC is the distance of wall from foot of ladder i.e, AC = 4.6 m
  • ∠ ACB is the angle of elevation of ladder i.e, ∠ ACB = 60°
  • BC = x is the length of ladder

Solution :

as we know ,

\implies\sf{cos\theta=\dfrac{adjacent\:side}{hypotenuse}}

so,

\implies\sf{cos\;60^{\circ}=\dfrac{4.6}{x}}

putting value of cos 60° = 1 / 2

\implies\sf{\dfrac{1}{2}=\dfrac{4.6}{x}}\\\\\\\implies\sf{x=4.6\times 2}\\\\\\\implies\boxed{\boxed{\sf{x=9.2\;\;m}}}

Hence, Height of ladder is 9.2 m .


BrainlyRaaz: Amazing ❤️
Answered by Anonymous
122

\rule{300}3

Given :-

  • The angle of elevation of a ladder leaning against a wall = 60°.

  • Distance of foot and ladder is 4.6 m.

To Find :-

  • The length of the ladder = ?

Diagram :-

\setlength{\unitlength}{1.6cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{A}}\put(7.7,1){\large\sf{C}}\put(10.6,1){\large\sf{B}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(8.8,0.7){\sf{\large{4.6m}}}\put(7.4,2){\sf{\large{wall}}}\put(9.3,2){\sf{\large{ladder}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\qbezier(9.8,1)(9.7,1.25)(10,1.4)\put(9.4,1.2){\sf\large{60^{\circ}$}}\end{picture}

  • AB = ladder

  • AC = wall

  • \angle B = 60°

  • BC = 4.6 m

Solution :-

\dashrightarrow\: \sf cos \:\theta = \dfrac{Adjacent\:side}{Hypotenuse}

\:\:

\dashrightarrow\: \sf cos\:60^{\circ} = \dfrac{4.6}{AB}

\:\:

\dashrightarrow\: \sf \dfrac{1}{2} = \dfrac{4.6}{AB}

\:\:

\dashrightarrow\: \sf AB = \dfrac{4.6 \times 2}{1}

\:\:

\dashrightarrow\: \underline{\boxed{\gray{ \textbf{AB = 9.2 \:m}}}} \red\bigstar

\:\:

Therefore, The height of the ladder is 9.2 m.

\rule{300}3

\gray\bigstar \large{\underline{\purple{ \textbf{Extra\: Shots\::-}}}}

\dagger\:\sf Trigonometric\:Values :\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & $\dfrac{1}{2} &$\dfrac{1}{\sqrt{2}} & $\dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & $\dfrac{\sqrt{3}}{2}&$\dfrac{1}{\sqrt{2}}&$\dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0&$\dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D$\hat{e}$fined\end{tabular}}

\rule{300}3


BrainlyRaaz: Perfect ✔️
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