find the parralel of latitude along which a journey of 166km makes a change of 4 degree in longitude give answer to the nearest degree

Answer 1

4 degrees = 1/90 of circumference
radius at latitude θ = r cosθ
r of earth is 6378 km

circumference at latitude θ is 2π*6378 cosθ

we want 1/90 (2π*6378 cosθ) = 116
so,
cosθ = (116*90)/(2π*6378) = 0.26
θ = 75°