Question

Apparent dips when dip circle is placed in two mutually perpendicular direction are ${30}^{o}and{45}^o$ What is actual dip at that place?

• A. $ta{n}^{-1}\left(2\right)$
• B. $ta{n}^{-1}\left(\frac{1}{2}\right)$
• C. $ta{n}^{-1}\left(\sqrt{2}\right)$
• D. ${60}^o$

Answer 1

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

As given in the question,

$co{t}^2\theta =co{t}^2{\theta }_1+co{t}^2{\theta }_2$

$co{t}^2\theta =co{t}^2{30}^0+co{t}^2{45}^0$

$co{t}^2\theta =3+1$

$co{t}^2\theta =4$

$cot\theta =2$

$tan\theta =\frac{1}{2}$

$\theta =ta{n}^{-1}\left(\frac{1}{2}\right)$