 | 1835 - 684 sider
...sides, angles, Sfc. of Triangles, or regular Poly* goni inscribed in, or circumscribed about it. (53.) THE sides of a triangle are proportional to the sines of the opposite angles. Let А, В, С be the angles, a, 6, с the sides opposite to them respectively of the triangle ABC. From С draw С D,... | |
 | George Peacock - 1845 - 480 sider
...there is always i triangle of which they may form two of the angles. and it follows, therefore, that the sides of a triangle are proportional to the sines of the opposite angles. foronTs'ide *^8- The f>undamental equations in Art. 875, will readily of a triangle furnish us with... | |
 | George Peacock - 1845 - 474 sider
...always " triangle of which they may form two of the angles. and it follows, therefore, that the tides of a triangle are proportional to the sines of the opposite angles. Expression 373. The fundamental equations in Art. 875, will readily for one side ' * of a triangle... | |
 | Harvey Goodwin - 1846 - 500 sider
...we must investigate certain formulae connecting the parts of a triangle. 104 PLANE TRIGONOMETRY. 29. The sides of a triangle are proportional to the sines of the opposite angles. FIG. 1. FIG. 2. CD Let ABC be a triangle. From any angular point A let fall the perpendicular AD on... | |
 | George Wirgman Hemming - 1851 - 176 sider
...TRIANGLES. PAGE 51. When three parts of a triangle are given, it can generally be solved 83 52 — 53. The sides of a triangle are proportional to the sines of the opposite angles 84 54. To express the cosine of an angle of a triangle in terms of the sides 85 56. On the solution... | |
 | Bartholomew Price - 1856 - 672 sider
...forces p, Q, R are proportional to the three lines OP, OQ, OR, or to OP, PR', R'OJ and since the three sides of a triangle are proportional to the sines of the opposite angles, therefore -J— = . Q = . R „ (29) sin OR' P sin a OP SIDOPE p QR or = = , sin a sin j3 sm y that... | |
 | Great Britain. Parliament. House of Commons - 1859 - 140 sider
...as the arc varies through a circumference. 10. Prove that in a plane triangle«a=6-+c2-26ccosA. 11. The sides of a triangle are proportional to the sines of the opposite angles. Prove this. 12. Investigate formula) for the solution of the different cases of plane triangles. 13.... | |
 | Royal University of Ireland - 1859 - 490 sider
...and less than four. Write the value of this ratio as far as five places of decimals. 17. Prove that the sides of a triangle are proportional to the sines of the opposite angles. 18. Given two sides and the included angle of a triangle, find the remaining side and angles. 19. Prove... | |
 | Denison Olmsted - 1860 - 492 sider
...component, it is not in the line of its action, because both forces act through the same point A. 46. Since the sides of a triangle are proportional to the sines of the opposite angles, these sines may also represent two components and their resultant. Thus, the sine of CAD corresponds... | |
 | Benjamin Greenleaf - 1862 - 532 sider
...THE SIDES AND ANGLES OF SPHERICAL TRIANGLES. 148. In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. Let А В С be any spherical triangle ; А, Д and С the angles opposite to its sides a, b, and c, respectively; and... | |
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The sides of a triangle are proportional to the sines of the opposite angles. 
