Page:Spherical Trigonometry (1914).djvu/38



40. Elements of a spherical triangle. A spherical triangle has six elements, namely the three sides $$a$$, $$b$$, $$c$$, and the three angles $$A$$, $$B$$, $$C$$. When any three of these are given, the form and dimensions of the triangle are completely determined, as there exist relations by means of which the other three elements can then be found. ‘These relations will be established in the present chapter.

They may conveniently be divided into two classes. In Section I. will be considered those formulae which involve four elements of the triangle; in Section II. those which involve five or six elements. .

41. Formulae involving four elements. There are four cases, according as the elements involved are:

I. Three sides and an angle.

II. Two sides and the angles opposite to them.

III. Two sides, the included angle, and another angle.

IV. Three angles and a side.