Definition
A trigonometric function of an acute angle in a right triangle, equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle.
Plain English
In a right-angled triangle, the tangent of one of the non-right angles is found by taking the side across from that angle and dividing it by the side next to it. It tells you how steep the angle is as a simple ratio of two sides.
Context Anchor
Seen in flight math involving climb angles, descent angles, glide paths, and other cases where an angle is connected to height change over distance.
Derivation
From the Latin tangere, meaning 'to touch.' The name comes from a line that just touches a circle at one point. That geometric idea carried into trigonometry, where the tangent ratio describes the slope of that touching line relative to the angle.
Why Pilots Care
Tangent shows up in practical flying math, such as calculating climb gradients, glide slopes, and obstacle clearance angles. Knowing what the ratio represents helps you read charts and performance figures with understanding rather than just plugging numbers into a formula.
Analogy
Think of a ramp. If the ramp rises 2 feet while moving 20 feet forward, the tangent of the ramp’s angle is 2 divided by 20.
Grounding Statement
Picture the airplane moving along a straight sloping path: the tangent of the angle compares the height change with the forward distance.
Intuition Check
Tangent here does not mean a side topic or going off course in conversation. It means a specific math comparison tied to an angle.
Example Sentence 1
To find the height of an obstacle a known distance away, the pilot multiplied that distance by the tangent of the climb angle.
Example Sentence 2
On the flight computer the tangent helped calculate how much the wind would affect the course.