Question

The true value of angle of dip at a place is \(60^{\circ}\), the apparent dip in a plane inclined at an angle of \(30^{\circ}\) with magnetic meridian is. (a) \(\tan ^{-1}(1 / 2)\) (b) \(\tan ^{-1} 2\) (c) \(\tan ^{-1}(2 / 3)\) (d) None of these

Short answer

The apparent dip in a plane inclined at an angle of \(30^{\circ}\) with the magnetic meridian is \(\tan^{-1}(\frac{\sqrt{3}}{2})\).

Step-by-step solution

Write down the given values

We have the following values given: True dip (δ) = \(60^{\circ}\) Inclination of the plane (β) = \(30^{\circ}\)

Substitute the given values in the formula

We have the formula: \( \tan\alpha = \tan\delta \sin\beta \). Substitute the given values of true dip and inclination of the plane: \(\tan\alpha = \tan(60^{\circ}) \sin(30^{\circ})\)

Calculate the value of tanα

Now, calculate the value of \(\tan\alpha\): \( \tan\alpha = \tan(60^{\circ}) \sin(30^{\circ}) = \sqrt{3} \times \frac{1}{2} = \frac{\sqrt{3}}{2} \)

Find the angle α

To find the angle α, we need to find the inverse tangent of the obtained value: \(\alpha = \tan^{-1}(\frac{\sqrt{3}}{2})\)

Choose the correct option

From the given choices, option (c) is \(\tan ^{-1}(2 / 3)\), which is not equal to \(\tan^{-1}(\frac{\sqrt{3}}{2})\). Therefore, the correct answer is option (d) None of these. The apparent dip in a plane inclined at an angle of \(30^{\circ}\) with the magnetic meridian is \(\tan^{-1}(\frac{\sqrt{3}}{2})\).