Question

The true angle of dip at a given place on earth is equal to ${53}^{\circ }$. If the plane of dip circle is at an angle of ${60}^{\circ }$ with the magnetic meridian, then the apparent angle of dip will be (Take $\tan {53}^{\circ }=\frac{4}{3})$

$[$0.77 Mark$]$

• A. ${\tan }^{-1}\left(\frac{8}{3}\right)$
• B. ${\tan }^{-1}\left(\frac{5}{4}\right)$
• C. ${\tan }^{-1}\left(\frac{4}{3}\right)$
• D. ${\tan }^{-1}\left(\frac{7}{3}\right)$

Answer 1

The correct option is A ${\tan }^{-1}\left(\frac{8}{3}\right)$

If apparent angle of dip is ${\delta }^{\prime }$ then,
$\tan {\delta }^{\prime }=\frac{\tan \delta }{\cos \varphi }$ where, $\delta$ is the true angle dip and $\varphi$ is inclination of plane of dip circle.
$\Rightarrow \tan {\delta }^{\prime }=\frac{\tan {53}^{\circ }}{\cos {60}^{\circ }}$
$=\frac{\frac{4}{3}}{\frac{1}{2}}=\frac{8}{3}$