Question

The dip circle is at $30º$ with a magnetic meridian. If the apparent dip is $60º$, then the true dip is

• A. $\begin{array}{l}\tan {}^{-1}\frac{1}{2}\end{array}$
• B. $\begin{array}{l}{\tan }^{-1}\sqrt{6}\end{array}$
• C. $\begin{array}{l}{\tan }^{-1}\sqrt{2}\end{array}$
• D. $0$

Answer 1

The correct option is A

$\begin{array}{l}\tan {}^{-1}\frac{1}{2}\end{array}$

Step 1: Given Data

Apparent dip $\delta \text{'}=60°$

The angle between the apparent dip and the magnetic meridian, $\theta =30°$

Let the true dip be $\delta$.

Step 2: Formula Used

$\tan \delta =\frac{\tan \delta \text{'}}{\cos \theta }$

Step 3: Calculate the Apparent Dip

We know that the expression for an apparent dip can be given as,

$$\begin{gathered} \tan \delta =\frac{\tan {\delta }^{\text{'}}}{\cos \theta } \\ =\frac{\tan 60°}{\cos 30°} \\ =\frac{{\displaystyle \sqrt{3}}}{{\displaystyle \frac{\sqrt{3}}{2}}} \\ =\frac{1}{2} \\ \therefore \delta ={\tan }^{-1}\frac{1}{2} \end{gathered}$$

Hence, the correct answer is option (A).