| Mathematics - 1835
...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.... | |
| George Peacock - Algebra - 1845
...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 - Algebra - 1845
...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 - Mathematics - 1846 - 468 pages
...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
...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
...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 - Bills, Legislative - 1859
...as the arc varies through a circumference. 10. Prove that in a plane triangleĞa=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.... | |
| 1859
...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 - Physics - 1860 - 456 pages
...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... | |
| Thomas Kimber - Mathematics - 1865 - 192 pages
...(A — B), cos. (A + B), cos. (A — В). What is the numerical value of sin. 30° ? 7. Prove that **the sides of a triangle are proportional to the sines of the opposite angles.** (Oct. 27iA. — Rev. Prof. HEAVISIDE.) 8. Find by means of rectangular co-ordinates, the length of... | |
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