Question

If the sun's angle of elevation in 30° and the height of the pole is 8m,then find the lenght of the shadow

Answer 1

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Answer 2

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.3 pt}\begin{picture}(100,100)(0,0)\put(0,10){\line(1,0){95}}\put(40,10){\line(0,1){55}}\put(95,10){\line(-1,1){85}}\multiput(0,65)(6,0){7}{\line(1,0){3}}\qbezier(88,16.856)(80.234,17.345)(81,10)\put(10,95){\circle*{20}}\put(25,35){ \sf{8\:m} }\put(22,45){ \bf{Pole} }\put(70,15){ \sf{30^{\circ}} }\put(10,105){ \bf Sun }\put(40,3){ \sf B }\put(40,68){ \sf A }\put(95,3){ \sf C }\end{picture}$

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Let the AB be the Pole & ∠ ACB be the Sun's angle of elevation i.e. 30°

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$\dashrightarrow\tt\:\:\tan(\theta)=\dfrac{Perpendicular}{Base}\\\\\\\dashrightarrow\tt\:\:\tan(30^{\circ})=\dfrac{AB}{BC}\\\\\\\dashrightarrow\tt\:\:\dfrac{1}{\sqrt{3}} = \dfrac{8\:m}{BC}\\\\\\\dashrightarrow\tt\:\:BC = 8\:m \times \sqrt{3}\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt BC = 8\sqrt{3}\:m}}$

⠀

$\therefore\:\underline{\textsf{Hence, Length of Shadow will be \textbf{8 \sqrt{\text3} m}}}.$

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