In casual reference, this is the same as elevation. This is the vertical distance from the average sea level to your point.

As you rise in altitude, for example, traveling from Los Angeles (~0ft altitude) to Denver (~5000ft) certain environmental factors change:

See high-altitude cooking and cosmic rays

To update Webster 1913's definition of an altitude for a geometric figure (2D or 3D):

  1. A perpendicular line segment from a vertex to the plane extension of the opposite face.
  2. A perpendicular line segment from a vertex to the line extension of the opposite side.
  3. A perpendicular line segment between parallel faces or sides, or between a face and a parallel side.
  4. The line extension of such line segment.
  5. The length of such line segment.

A pictoral example of an altitude (def. D) of a triangle ABC.
                     |
                     |
                     |C
                    /|\
                  /  a \
                /    l  \
              /      t   \
            /        i    \
          /          t     \
        /            u      \
      /              d       \
    /                e        \
  /                  |         \
A--------------------+----------B
                     |
                     |



Sources: (1) Merriam-Webster's Collegiate Dictionary © 2001, (2)
"Vectors and Transformations in Plane Geometry" by Philippe Tondeur, Publish or Perish, Inc. 1993

In modern Euclidean geometry, a triangle's area, K, given by Heron's formula, and its sidelengths a, b, and c are considered primary. Therefore, the altitude from a vertex to the opposite has the form:

      hA   = 2K/a

where A is the vertex and a is the sidelength opposite A.

Altitudes are important in many geometric proofs. They are also used constructively to create circles within triangles and quadrilaterals.

A few key facts about altitudes:

Al"ti*tude (#), n. [L. altitudo, fr. altus high. Cf. Altar, Haughty, Enhance.]

1.

Space extended upward; height; the perpendicular elevation of an object above its foundation, above the ground, or above a given level, or of one object above another; as, the altitude of a mountain, or of a bird above the top of a tree.

2. Astron.

The elevation of a point, or star, or other celestial object, above the horizon, measured by the arc of a vertical circle intercepted between such point and the horizon. It is either true or apparent; true when measured from the rational or real horizon, apparent when from the sensible or apparent horizon.

3. Geom.

The perpendicular distance from the base of a figure to the summit, or to the side parallel to the base; as, the altitude of a triangle, pyramid, parallelogram, frustum, etc.

4.

Height of degree; highest point or degree.

He is [proud] even to the altitude of his virtue. Shak.

5.

Height of rank or excellence; superiority.

Swift.

6. pl.

Elevation of spirits; heroics; haughty airs.

[Colloq.]

Richardson.

The man of law began to get into his altitude. Sir W. Scott.

Meridian altitude, an arc of the meridian intercepted between the south point on the horizon and any point on the meridian. See Meridian, 3.

 

© Webster 1913.

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