$\begin{array}{1 1} (A) \theta = \sin^{-1} \large (\frac{8}{5}) \\(B) \theta = \cos^{-1} \large (\frac{8}{5}) \\(C) \theta = \tan^{-1} \large (\frac{8}{5}) \\ (D) \theta = \tan^{-1} \large (\frac{5}{8}) \\ \end{array}$

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The vertical component of the earth's magnetic field is given by $B_v = B \sin \theta I$ and the horizontal component by $B_h = B \cos \theta I$

$\Rightarrow \large\frac{B_v}{B_h} = \large\frac{B \sin \theta I}{B \cos \theta I} $$ \rightarrow \tan \theta =\large\frac{B_v}{B_h}$

$\Rightarrow \tan \theta = \large\frac{40}{25} $$ =\large\frac{8}{5}$$ \rightarrow \theta = tan^{-1} \large (\frac{8}{5})$ $ \rightarrow \theta = 58 ^{\circ}$

This is the angle that the magnetic field makes with Earth's magnetic meredian. For any magnet to be stable in equilibrium, it needs to stay in this direction, thus making this angle with the horizontal plane.

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