Q. 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) $\cot^2\theta = \cot^2\theta_1 + \cot^2\theta_2$
B) $\tan^2\theta = \tan^2\theta_1 + \tan^2\theta_2$
C) $\cot^2\theta = \cot^2\theta_1 - \cot^2\theta_2$
D) $\tan^2\theta = \tan^2\theta_1 - \tan^2\theta_2$
Explanation
[Solution] $\cot\theta_1 = H\cos\alpha/V$ and $\cot\theta_2 = H\sin\alpha/V$; adding squares gives $\cot^2\theta = \cot^2\theta_1 + \cot^2\theta_2$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.