Abstract
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°.
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