Question

The values of the apparent angles of dip in two planes at right angles to each other are $30$ and $45$, Then the true value of angle of dip at the place is ________

• A. ${\tan }^{-1}1$
• B. ${\tan }^{-1}2$
• C. ${\cot }^{-1}2$
• D. ${\cot }^{-1}4$

Answer 1

Answer: (C)

${\cot }^{-1}2$

$\text{Solution}:$

$tan{30}^0=\frac{tan\delta }{cos\theta }$, or $cos\theta =\frac{tan\delta }{tan{30}^o}=\sqrt{(}3)tan\delta$

Again, $tan{45}^0=\frac{tan\delta }{sin\theta }$ or $sin\theta =tan\delta$

We know, $si{n}^2\theta +co{s}^2\theta =1$

$\therefore ta{n}^2\delta +3ta{n}^2\delta =1$ or $ta{n}^2\delta =\frac{1}{4}$ or $tan\delta =\frac{1}{2}$ or $\frac{1}{cos\delta }=\frac{1}{2}$ or $\delta =co{t}^{-1}\left(2\right)$

$\text{Hence C is the correct option}$