In a certain position, the needle of a dip circle indicates an apparent dip of 45^ . When the circle is rotated by 90^ , the apparent dip shown is 53^ . Determine the true dip.

Step-by-step solution

Let the true dip be . The apparent dips in two mutually perpendicular planes are ₁ = 45^ and ₂ = 53^ . The relation between true dip and apparent dips is given by: ^2 = ^2 ₁ + ^2 ₂ Substituting the given values: ^2 = ^2 45^ + ^2 53^ ^2 = (1)^2 + ( 3 4 )^2 ^2 = 1 + 9 16 = 25 16 = 5 4 = 4 5 = 0.8 = ⁻¹(0.8) 39^