Question

The true value of angle of dip at a place is ${60}^{\circ }$. The apparent dip, in a plane inclined at an angle of ${30}^{\circ }$ with the magnetic meridian is:

• A. ${\tan }^{-1}\left(\frac{1}{2}\right)$
• B. ${\tan }^{-1}\left(2\right)$
• C. ${\tan }^{-1}\left(\frac{2}{3}\right)$
• D. ${\tan }^{-1}\left(\frac{1}{3}\right)$

Answer 1

The correct option is B ${\tan }^{-1}\left(2\right)$

$\delta \to \text{Dip Angle}$

${\delta }_{True}={60}^{\circ }$

${\delta }_{App}=?$

Angle between the given plane and magnetic meridian, $\theta ={30}^{\circ }$

Now, $\tan \left({\delta }_{App}\right)=\frac{\tan \left({\delta }_{Real}\right)}{\cos \theta }$

$\therefore \tan \left({\delta }_{App}\right)=\frac{\tan {60}^{\circ }}{\cos {30}^{\circ }}=\frac{\sqrt{3}}{\sqrt{3}/2}=2$

$\therefore {\delta }_{App}={\tan }^{-1}\left(2\right)$

Hence, option $\left(B\right)$ is the correct answer.