From COS φ = 0.6, namely φ = 53 degrees, we can get TG φ = 1.3 1. I don't know how to calculate φ and TG φ, you can solve it.
Cos φ = 0.6, that is φ = 53 degrees, which is obtained by using the inverse trigonometric function. 53 degrees is not an accurate approximation. Similarly, it is known that cos φ = 0.6, and it is easy to draw a right triangle with the tangent value of the sphere. For the solution of inverse trigonometric function, please refer to "Table for Mathematics" arccos0.6=53 degrees.