A compass needle points 30° west of north on a horizontal table. In the vertical plane containing this direction, it points 30° below horizontal. If the compass is instead kept in the vertical plane containing the true north-south direction, the needle makes what angle with the horizontal?
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Question

A compass needle points 30° west of north on a horizontal table. In the vertical plane containing this direction, it points 30° below horizontal. If the compass is instead kept in the vertical plane containing the true north-south direction, the needle makes what angle with the horizontal?

Options

G1 Physics · Accepted Answer

The horizontal compass direction gives declination 30°. In the vertical magnetic-meridian plane the apparent dip is 30°, so Bᵥ/Bₕ=tan 30°. Resolving the horizontal component toward true north gives tanδ = 2/3. Hence the required angle is tan⁻¹(2/3), option B.