 | Thomas Grenfell Vyvyan - 1882 - 150 pages
...equations connectingthese six quantities. One of these equations is A + B+ C= 180°.. ..Euc. i. 32. 40. The sides of a triangle are proportional to the sines of the angles opposite to them. Let ABC be a triangle and let B be one of the acute angles. (See the figures... | |
 | William James Browne - Mechanics - 1883 - 218 pages
...have only one resultant, yet any given resultant can have many FIG. 12. sets of components. * Since the sides of a triangle are proportional to the sines of the opposite angles, if three forces acting at a point are in equilibrium, each force is proportional to the sine of the... | |
 | George Albert Wentworth - Trigonometry - 1884 - 330 pages
...we may obtain, in the same way, sin C a__ e sin C Hence the Law of Sines, which may be thus stated : The sides of a triangle are proportional to the sines of the opposite angles. If we regard these three equations as proportions, and take them by alternation, it will be evident... | |
 | Thomas Tredgold - 1885 - 412 pages
...point A, are in the proportion of the lines AE, AF, and FE (because FE is equal to AG). But because the sides of a triangle are proportional to the sines of the opposite angles, the strains are proportional to the sines of the angles AFE, AEF, and FAE. But the sine of AFE is the... | |
 | George Albert Wentworth - 1887 - 206 pages
...obtain, in the same way, sin B sin C a e .sin A sin 0 Hence the Law of Sines, which may be thus stated : The sides of a triangle are proportional to the sines of the opposite angles. If we regard these three equations as proportions, and take them by alternation, it will be evident... | |
 | George Albert Wentworth - 1887 - 346 pages
...in the same way, sin .B ein C a. e sin .4 sin C Hence the Law of Sines, which may be thus stated : The sides of a triangle are proportional to the sines of the opposite angles. If we regard these three equations as proportions, and take them by alternation, it will be evident... | |
 | Sidney Luxton Loney - Dynamics - 1891 - 230 pages
...a, /3 with it, and through D draw parallels to complete the parallelogram ABDC as in Art. 12. Since the sides of a triangle are proportional to the sines of the opposite angles, we have AB BD AD sin ADB ~ sin BAD ~ sin ABD , ie. AB BD AD sin |8 sin a sin (a + /?) ' Hence the component... | |
 | Nathan Fellowes Dupuis - Geometry - 1894 - 313 pages
...be a diameter. Then z_D=^A, (106°, Cor. i) and ACBD=~~|. At and from symmetry, sin A sin B sin C' Hence the sides of a triangle are proportional to...the feet of the perpendiculars PP' and QQ'. Now P'Q' = PQcos(PQ.P'Q'). .'. the projection of any segment on a given line is the segment multiplied by the... | |
 | George Albert Wentworth - Navigation - 1895 - 436 pages
...in the same way, b sin Б u sin A e sin C sin C Hence the Law of Sines, which may be thus stated : The sides of a triangle are proportional to the sines of the opposite angles. If we regard these three equations as proportions, and take them by alternation, it will be evident... | |
 | Richard Glazebrook, Sir Richard Tetley Glazebrook - Hydrostatics - 1895 - 682 pages
...forces P, Q, R are proportional to the sides BC , CA and AB of the triangle ABC respectively. Moreover the sides of a triangle are proportional to the sines of the opposite angles. Thus the forces are proportional to the sines of the angles of the triangle which are opposite to them.... | |
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The sides of a triangle are proportional to the sines of the opposite angles. 
