Question

The plane of a dip circle is set in the geographic meridian and the apparent dip is δ₁. It is then set in a vertical plane perpendicular to the geographic meridian. The apartment dip angle is δ₂. The declination at the place is

(a) θ = tan^–1(tan√δ₁ × tan√δ₂)

(b) θ = tan^–1(tan√δ₁ + tan√δ₂)

(c) θ = tan^–1 [(tan√δ₁)/(tan√δ₂)]

(d) θ = tan^–1 [(tan√δ₂)/(tan√δ₁)]

Answer 1

The correct option (c) θ = tan^–1 [(tan√δ₁)/(tan√δ₂)]

Explanation:

The diagram can be drawn as

apparent dip in geographic meridian is δ₁

∴   tanδ₁ = [V / (H cosθ)]

apparent dip in vertical plane perpendicular to geographic meridian is δ₂

∴  tanδ₂ = [V/{H cos(90 – θ)}] = [V/(H sinθ)]

∴  [(tanδ₁)/(tanδ₂)] = [{V/(H cosθ)}/{V/(H sinθ)}] = tanθ

θ = tan^–1 [(tanδ₁) / (tanδ₂)]