Which formula expresses apparent dip as part of finding it?

• A. tan(a) = tan(second) sin(first)
• B. tan(a) = tan(first) sin(second)
• C. tan(a) = sin(first) / tan(second)
• D. tan(a) = tan(second) cos(first)

Answer: (A)

Apparent dip depends on how steep the plane actually tilts and on the direction you measure it in. When you project the plane into the vertical plane that contains your measurement direction, the slope you observe (the apparent dip) grows with the true dip but is reduced by how far your measurement direction is from the strike. The geometric relationship is tan(apparent dip) = tan(true dip) × sin(angle between the measurement direction and the strike). Here, the true dip is the steepest angle the plane makes with horizontal, and the angle is measured from the strike toward the dip direction.

The correct expression matches tan(apparent) = tan(true dip) × sin(angle). That’s why tan(a) = tan(second) sin(first) is the right form: it uses the true dip in the tangent and multiplies by the sine of the angle from strike. Along the strike (angle zero) the apparent dip is zero; along the dip direction (angle ninety degrees) the apparent dip equals the true dip. The other forms don’t align with this projection geometry.