Acute Angle

Pronunciation: /əˈkyut ˈæŋ gəl/ ?

Figure 1: Acute angles measure < 90° Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Manipulative 1: Classes of angles. Created with GeoGebra. Click to see gadget full screen.

Angles are divided into four classes according to their measure. An acute angle is an angle that measures less than 1/4 of a full circle[1][2]. Classes of Angles Degree Measure Radian Measure Class Name α<90° α<π/2 rad. Acute angle α=90° α=π/2 rad. Right angle 90°<α<180° π/2<α<π rad. Obtuse angle α=180° α=π rad. Straight angle 180<α<360° π<α<2π rad. Reflex angle α=360° α=2π rad. Full angle Table 1: Classes of angles Click on the blue point in the manipulative and drag it to change the figure.

References

1. acute angle. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-12-21). http://www.merriam-webster.com/dictionary/acute angle.
2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry, pg 2. D. Van Nostrand Company, 1908. (Accessed: 2010-01-02). http://www.archive.org/stream/mathengineer00kellrich#page/2/mode/1up/search/acute.
3. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid, 10th Edition, pg 4. Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co., 1890. (Accessed: 2010-01-02). http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/4/mode/1up/search/acute.

Printed Resources

Cite this article as:

Acute Angle. 2010-01-01. All Math Words Encyclopedia. Life is a Story Problem.org. http://www.allmathwords.org/en/a/acuteangle.html.

Translations

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Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem.org and are licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Revision History

2010-01-01: Added reference to Euclid's Elements, Expanded table of angle classes. (McAdams, David.)
2008-09-16: Changed text on classes of angles to a table. Changed images 2 and 3 to one manipulative (McAdams, David.)
2008-03-03: Revised other resources, added reference to radians (McAdams, David.)
2007-07-16: Expanded keyword 'acute' to include 'angle' (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)