Acute Angle

Pronunciation: /əˈkjut ˈæŋ.gəl/ Explain

Figure 1: Acute angles measure < 90° Click on the blue point and drag it to change the figure. Can you find all 5 angle classes represented? Manipulative 1 - Angle Classes Created with GeoGebra.

Angles are divided into six classes according to their measure. An acute angle is an angle that measures less than 1/4 of a full circle[2][3]. 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

References

1. McAdams, David E.. All Math Words Dictionary, acute angle. 2nd Classroom edition 20150108-4799968. pg 10. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 2. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 6/12/2018. http://www.archive.org/stream/mathengineer00kellrich#page/2/mode/1up/search/acute. Buy the book
3. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. 10th Edition. pg 4. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 6/12/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/4/mode/1up/search/acute. Buy the book

Cite this article as:

McAdams, David E. Acute Angle. 4/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/acuteangle.html.

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 LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/11/2019: Changed equations and expressions to new format. (McAdams, David E.)
1/7/2019: Removed extraneous text about manipulative. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/12/2018: Removed broken links, changed Geogebra links to work with Geogebra 5, updated license, implemented new markup. (McAdams, David E.)
1/1/2010: Added reference to Euclid's Elements, Expanded table of angle classes. (McAdams, David E.)
9/16/2008: Changed text on classes of angles to a table. Changed images 2 and 3 to one manipulative (McAdams, David E.)
3/3/2008: Revised other resources, added reference to radians. (McAdams, David E.)
7/16/2007: Expanded keyword 'acute' to include 'angle'. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)