The values of the apparent angles of dip in t | vedclass

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(B) Let $\phi$ be the true angle of dip,and $\alpha_1$ and $\alpha_2$ be the apparent angles of dip in two mutually perpendicular planes.The relations

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

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(B) Let $\phi$ be the true angle of dip,and $\alpha_1$ and $\alpha_2$ be the apparent angles of dip in two mutually perpendicular planes.The relationship between the true angle of dip and the apparent angles of dip is given by the formula:$\cot^2 \phi = \cot^2 \alpha_1 + \cot^2 \alpha_2$Given:$\alpha_1 = 45^{\circ}$$\alpha_2 = 30^{\circ}$Substituting the values:$\cot^2 \phi = \cot^2 45^{\circ} + \cot^2 30^{\circ}$Since $\cot 45^{\circ} = 1$ and $\cot 30^{\circ} = \sqrt{3}$:$\cot^2 \phi = (1)^2 + (\sqrt{3})^2$$\cot^2 \phi = 1 + 3 = 4$Taking the square root on both sides:$\cot \phi = 2$Therefore,the true angle of dip is:$\phi = \cot^{-1}(2)$

The values of the apparent angles of dip in two planes at right angles to each other are $45^{\circ}$ and $30^{\circ}$ respectively. The true value of the angle of dip at the place is ............

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