...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....

...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...

...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...

...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...

...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...

...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...

...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...

...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....

...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...

.... bc An exactly similar proof would shew that sin A sin B Hence ab sin A — sinB _ sin C abc ' 2. This relation between the sides and the sines of the opposite angles furnishes us with two equations involving the six parts of which a triangle is composed, viz. the three...