. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . a b sin A and b, no solution. one solution (right triangle). two solutions. one solution. These results may be obtained algebraically thus: We have a2 = b2 + c2-2bccosA (Art. 96) b cos A ± V a2 ? b2 sin2 A, OBLIQUE TRIANGLES, 175 giving two roots, real and unequal, equal or imaginary,according as a >, =, or < b sin A. A discussion of these two values of c gives the sameresults as are found in the above four cases. We leavethe discussion as an exercise for the student.

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. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . a b sin A and b, no solution. one solution (right triangle). two solutions. one solution. These results may be obtained algebraically thus: We have a2 = b2 + c2-2bccosA (Art. 96) b cos A ± V a2 ? b2 sin2 A, OBLIQUE TRIANGLES, 175 giving two roots, real and unequal, equal or imaginary,according as a >, =, or < b sin A. A discussion of these two values of c gives the sameresults as are found in the above four cases. We leavethe discussion as an exercise for the student. Note. — When two sides and the angle opposite the greater are given, there canbe no ambiguity, for the angle opposite the less must be acute. When the given angle is a right angle or obtuse, the other two angles are bothacute, and there can be no ambiguity. In the solution of triangles there can be no ambiguity, except when an angle isdetermined by the sine or cosecant, and in no case whatever when the triangle hasa right angle. Ex. 1. Given a = 7, 6 = 8, A = 27°

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Keywords: ., bookcentury1900, bookdecade1900, booksubjecttrigono, bookyear1902