Definition
A trigonometric function of an angle in a right triangle, defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Written as tan θ = opposite ÷ adjacent.
Plain English
A number that describes how steep an angle is. For any angle in a right-angled triangle, you take the side across from the angle and divide it by the side next to it. The result is the tangent of that angle.
Context Anchor
Seen in maintenance math, layout, and geometry problems when an angle must be changed into a usable distance or a distance must be changed into an angle.
Derivation
From the Latin tangere, meaning 'to touch.' The name comes from geometry: the tangent line touches a circle at a single point. In trigonometry, the tangent function is built from this same idea of a line touching a circle at the angle being measured.
Why Pilots Care
Technicians use tangent calculations when laying out sheet metal repairs, figuring rigging angles, checking control surface travel, and solving structural geometry problems. Getting the ratio wrong produces parts that don't fit or rigging that's out of tolerance.
Intuition Check
Tan does not mean the color tan or skin darkened by the sun here. In this context, tan is a math term meaning the tangent of an angle.
Example Sentence 1
To find the height of the rudder hinge offset, the technician used tan of the deflection angle multiplied by the arm length.
Example Sentence 2
Apply the tan function to determine the slope of the wing surface.