The Collaborative International Dictionary of English v.0.48:

Acute \A*cute"\, a. [L. acutus, p. p. of acuere to sharpen, fr.
   a root ak to be sharp. Cf. Ague, Cute, Edge.]
   1. Sharp at the end; ending in a sharp point; pointed; --
      opposed to blunt or obtuse; as, an acute angle; an
      acute leaf.
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   2. Having nice discernment; perceiving or using minute
      distinctions; penetrating; clever; shrewd; -- opposed to
      dull or stupid; as, an acute observer; acute remarks,
      or reasoning.
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   3. Having nice or quick sensibility; susceptible to slight
      impressions; acting keenly on the senses; sharp; keen;
      intense; as, a man of acute eyesight, hearing, or feeling;
      acute pain or pleasure.
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   4. High, or shrill, in respect to some other sound; --
      opposed to grave or low; as, an acute tone or accent.
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   5. (Med.) Attended with symptoms of some degree of severity,
      and coming speedily to a crisis; -- opposed to chronic;
      as, an acute disease. AS
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   Acute angle (Geom.), an angle less than a right angle.
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   Syn: Subtile; ingenious; sharp; keen; penetrating; sagacious;
        sharp-witted; shrewd; discerning; discriminating. See
        Subtile.
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The Collaborative International Dictionary of English v.0.48:

Angle \An"gle\ ([a^][ng]"g'l), n. [F. angle, L. angulus angle,
   corner; akin to uncus hook, Gr. 'agky`los bent, crooked,
   angular, 'a`gkos a bend or hollow, AS. angel hook, fish-hook,
   G. angel, and F. anchor.]
   1. The inclosed space near the point where two lines meet; a
      corner; a nook.
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            Into the utmost angle of the world.   --Spenser.
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            To search the tenderest angles of the heart.
                                                  --Milton.
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   2. (Geom.)
      (a) The figure made by. two lines which meet.
      (b) The difference of direction of two lines. In the lines
          meet, the point of meeting is the vertex of the angle.
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   3. A projecting or sharp corner; an angular fragment.
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            Though but an angle reached him of the stone.
                                                  --Dryden.
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   4. (Astrol.) A name given to four of the twelve astrological
      "houses." [Obs.] --Chaucer.
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   5. [AS. angel.] A fishhook; tackle for catching fish,
      consisting of a line, hook, and bait, with or without a
      rod.
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            Give me mine angle: we 'll to the river there.
                                                  --Shak.
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            A fisher next his trembling angle bears. --Pope.
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   Acute angle, one less than a right angle, or less than
      90[deg].

   Adjacent or Contiguous angles, such as have one leg
      common to both angles.

   Alternate angles. See Alternate.

   Angle bar.
      (a) (Carp.) An upright bar at the angle where two faces of
          a polygonal or bay window meet. --Knight.
      (b) (Mach.) Same as Angle iron.

   Angle bead (Arch.), a bead worked on or fixed to the angle
      of any architectural work, esp. for protecting an angle of
      a wall.

   Angle brace, Angle tie (Carp.), a brace across an
      interior angle of a wooden frame, forming the hypothenuse
      and securing the two side pieces together. --Knight.

   Angle iron (Mach.), a rolled bar or plate of iron having
      one or more angles, used for forming the corners, or
      connecting or sustaining the sides of an iron structure to
      which it is riveted.

   Angle leaf (Arch.), a detail in the form of a leaf, more or
      less conventionalized, used to decorate and sometimes to
      strengthen an angle.

   Angle meter, an instrument for measuring angles, esp. for
      ascertaining the dip of strata.

   Angle shaft (Arch.), an enriched angle bead, often having a
      capital or base, or both.

   Curvilineal angle, one formed by two curved lines.

   External angles, angles formed by the sides of any
      right-lined figure, when the sides are produced or
      lengthened.

   Facial angle. See under Facial.

   Internal angles, those which are within any right-lined
      figure.

   Mixtilineal angle, one formed by a right line with a curved
      line.

   Oblique angle, one acute or obtuse, in opposition to a
      right angle.

   Obtuse angle, one greater than a right angle, or more than
      90[deg].

   Optic angle. See under Optic.

   Rectilineal or Right-lined angle, one formed by two right
      lines.

   Right angle, one formed by a right line falling on another
      perpendicularly, or an angle of 90[deg] (measured by a
      quarter circle).

   Solid angle, the figure formed by the meeting of three or
      more plane angles at one point.

   Spherical angle, one made by the meeting of two arcs of
      great circles, which mutually cut one another on the
      surface of a globe or sphere.

   Visual angle, the angle formed by two rays of light, or two
      straight lines drawn from the extreme points of an object
      to the center of the eye.

   For Angles of commutation, draught, incidence,
   reflection, refraction, position, repose, fraction,
      see Commutation, Draught, Incidence, Reflection,
      Refraction, etc.
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WordNet (r) 3.0 (2006):

acute angle
    n 1: an angle less than 90 degrees but more than 0 degrees