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If \Theta _{1} and \Theta _{2} be the apparent angles of dip observed in two verical planes at right angles to each other, then the true angle of  dip \Theta is given by:-

  • Option 1)

    \tan ^{2}\Theta =\tan ^{2}\Theta _{1}+\tan ^{2}\Theta _{2}

  • Option 2)

    \cot ^{2}\Theta =\cot ^{2}\Theta _{1}-\cot ^{2}\Theta _{2}

  • Option 3)

    \tan ^{2}\Theta =\tan ^{2}\Theta _{1}-\tan ^{2}\Theta _{2}

  • Option 4)

    \cot ^{2}\Theta =\cot ^{2}\Theta _{1}+\cot ^{2}\Theta _{2}

 

Answers (1)

best_answer

 

Angle of Inclination or Dip -

It is the angle between the direction of intensity of total magnetic field of earth and a horizontal line in the magnetic meridian.

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 \tan \theta _{1}=\frac{tan\theta }{cos\alpha }\:and\:\tan \theta _{2}=\frac{\tan \theta }{\cos (90-\alpha )}\\ \tan \theta _{2}=\frac{\tan \theta }{\sin \alpha }

CO+CO+^{2} \Theta_{1}+CO+^{2} \Theta_{2}=\frac{\sin ^{2}\alpha+\cos ^{2}\alpha } {\tan ^{2}\theta }=\cot ^{2}\theta


Option 1)

\tan ^{2}\Theta =\tan ^{2}\Theta _{1}+\tan ^{2}\Theta _{2}

This solution is incorrect 

Option 2)

\cot ^{2}\Theta =\cot ^{2}\Theta _{1}-\cot ^{2}\Theta _{2}

This solution is incorrect 

Option 3)

\tan ^{2}\Theta =\tan ^{2}\Theta _{1}-\tan ^{2}\Theta _{2}

This solution is incorrect 

Option 4)

\cot ^{2}\Theta =\cot ^{2}\Theta _{1}+\cot ^{2}\Theta _{2}

This solution is correct 

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