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Integer-sided triangles with an angle of 120°

Published online by Cambridge University Press:  22 September 2016

Keith Selkirk
Keith Selkirk*
Affiliation:
School of Education, University of Nottingham
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Extract

John Gilder’s article on integer-sided triangles in the December 1982 Gazette [1] immediately suggests the question of what other triangles with integer sides have an angle which is a whole number of degrees. This is very simple to answer, for if the sides are integers, the cosine formula implies that the cosines of all three angles must be rational. Only angles of 60°, 90° and 120° fulfil this condition for the appropriate range of values, and it follows that, apart from the familiar right-angled triangle and Gilder’s case of the 60° angled triangle, the only other possible case is a triangle with an angle of 120°.

Type
Research Article
Information
The Mathematical Gazette , Volume 67 , Issue 442 , December 1983 , pp. 251 - 255
Copyright
Copyright © Mathematical Association 1983

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References

1. Gilder, John, Integer-sided triangles with an angle of 60°. Math. Gaz. 66, 261–266 (1982).Google Scholar
2. Losch, A., The economics of location. Yale University Press (1954).Google Scholar
3. Selkirk, K. E., Pattern and place. Cambridge University Press (1982).Google Scholar