Answer 1

Let the true value of dip be Φ. When the magnet is kept 45° aligned with declination 30°, the horizontal component of Earth’s magnetic field.
B’_H = B_H cos 30° Whereas, the vertical component remains unchanged.
∴ For an apparent dip of 45°,
tan 45° = `"B"_"V"^′/"B"_"H"^′="B"_"V"/("B"_"H"cos30°)="B"_"V"/"B"_"H"xx1/(cos30°)`
But, real value of dip is,
tan Φ = `"B"_"V"/"B"_"H"`

∴ tan 45° = `tanΦ/(cos30°)`

∴ tan Φ = tan 45° × cos 30°

= `1xxsqrt3/2`

∴ Φ = tan⁻¹ (0.866)

The true value of angle of dip is tan⁻¹ (0.866).