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9th Class Mathematics Geometry Question Bank Geometry

  • question_answer
    Consider a cube ABCD - PQRS, if 0 is the angle between diagonal BS and the plane PQRS, then  the value of tan 0 is equal to

    A) \[1\]             

    B) \[\sqrt{2}\]

    C) \[\frac{1}{\sqrt{2}}\]

    D) \[\sqrt{3}\]

    Correct Answer: C

    Solution :

     Let x be the length of the cube \[\therefore \]  \[BQ=x\] and        \[SQ=\sqrt{{{x}^{2}}+{{x}^{2}}}\]                 \[=\sqrt{2}\,x\] From right angled \[\Delta \,BSQ\]                 \[\tan \theta =\frac{BQ}{SE}\]                 \[=\frac{x}{\sqrt{2x}}=\frac{1}{\sqrt{2}}\]


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