Question

If $\theta_1$ and $\theta_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\theta$ is given by :

• A. $\tan^2 \theta = \tan^2 \theta_1 + \tan^2 \theta_2$
• B. $\cot^2 \theta = \cot^2 \theta_1 - \cot^2 \theta_2$
• C. $\tan^2 \theta = \tan^2 \theta_1 - \tan^2 \theta_2$
• D. $\cot^2 \theta = \cot^2 \theta_1 + \cot^2 \theta_2$

Answer 1

Answer: (D)

$\cot^2 \theta = \cot^2 \theta_1 + \cot^2 \theta_2$

Answer 2

$\tan \theta_1 = \frac{\tan \theta}{ \cos \alpha}$
$\Rightarrow \tan \theta_2 =\frac{\tan \theta }{\cos (90 - \alpha )}= \frac{\tan \theta}{\sin \alpha}$
$\Rightarrow \sin^2 \alpha + \cos^2 \alpha = 1$
$\Rightarrow \cot^2 \theta_2 + \cot^2 \theta_1 = \cot^2 \theta$