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The shadow of a tower standing …

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The shadow of a tower standing on a level ground is found to be 40m longer when the sun's altitude is 30degree than when it is 60degree . find the height of tower

    • Posted by Yash Rana 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago


    In {tex}\triangle A B C,{/tex} {tex}\tan 60 ^ { \circ } = \frac { A B } { B C }{/tex} 
    {tex}\Rightarrow \quad A B = \sqrt { 3 } B C{/tex}  .....(i)
    In {tex}\triangle A B D,{/tex}  
    {tex}\tan 30 ^ { \circ } = \frac { A B } { B C + 40 }{/tex} 
    {tex}\frac{ 1}{√3}=\frac{AB}{BC+40}=\frac{√3BC}{BC+40}{/tex}
    3BC = BC + 40
    BC = 20, Hence from (i) we get
    AB = 20√3 = 20 {tex}\times{/tex} 1.73 = 34.6 meter

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