 | John Farrar - 1834 - 504 sider
...not commonly observed, and which only serves to connect our two triangles. The process is simple, for in every spherical triangle the sines of the angles are proportional to the siws of the opposite sides. Thus, in our triangle ZP8 referred to the . sin P' . sin Z' true places,... | |
 | John Charles Snowball - 1837 - 322 sider
...A + BC<ir. CHAPTER II. FORMULjE CONNECTING THE SIDES AND ANGLES OF A SPHERICAL TRIANGLE. 28. IN any spherical triangle, the sines of the angles are proportional to the sines of the sides respectively opposite: or, ABC being the triangle, sin A sin B sin С sin BC sin AC sin AB... | |
 | De Volson Wood - 1885 - 298 sider
...result. CHAPTER V. OBL1QUE ANGLED TR1ANGLE8 8OLVED BY MEAN8 OF R1GHT ANGLED TMANGLE8. 75. In a spherieal triangle the sines of the angles are proportional to the sines of the sides opposite. ln the spherical triangle ABC, let fall the perpendicular BD from any angle B upon... | |
 | De Volson Wood - 1887 - 272 sider
...required result. CHAPTEE V. OBLIQUE ANGLED TBIANGLES SOLVED BY MEANS OP BIGHT ANGLED TBIANGLES. 75. In a spherical triangle the sines of the angles are proportional to the sines of the sides opposite. In the spherical triangle ABC, let fall the perpendicular BD from any angle В... | |
 | Theodore Graham Gribble - 1891 - 482 sider
...tan ± (a ~ 6) : ten % c ; .'. tan ic = sin i_ (A + B) x tan .', (a ~ b) •+• sin | (A ~ B) (78) In every spherical triangle the sines of the angles are proportional to the sines of the opposite sides. A/ sin bx sin c • (72) . , T, / sin (s — a) * sin |s — c] . (73) • (74)... | |
 | John Whitelaw - 1902 - 638 sider
...= • sin c Cos b = cot A x cot c sin A Oblique Spherical Triangles (Fig. 230). Rule of Sines. — In every spherical triangle the sines of the angles are proportional to the sines of the opposite sides. c Fig. 229. Right-angled Spherical Triangles. Fig. 230. Oblique Spherical Triangles.... | |
 | John Whitelaw - 1902 - 634 sider
...b = cot A x cot c Cos c=„ cos c sin A Oblique Spherical Triangles (Fig. 230). Rule of Sines.—In every spherical triangle the sines of the angles are proportional to the sines of the opposite sides. Fig. 229. Right-angled Spherical Triangles. Fig. 230. Oblique Spherical Triangles.... | |
 | John Whitelaw - 1916 - 582 sider
...— 335 sin c Cos b = cot A x cot c sin A Oblique Spherical Triangles (Fig. 230). Rule of Sines. — In every spherical triangle the sines of the angles are proportional to the sines of the opposite sides. t Fig. 229. Right-angled Spherical Triangles. Fig- 230. Oblique Spherical Triangles.... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - 1916 - 348 sider
...31' 36", у = 67° 16' 22". OBLIQUE SPHERICAL TRIANGLES 121. Sine theorem (Law of sines). — In any spherical triangle, the sines of the angles are proportional to the sines of the opposite sides. Proof. Let ABC, Fig. 123, be a spherical triangle. Construct the great circle arc... | |
 | James Atkins Bullard, Arthur Kiernan - 1922 - 252 sider
...Therefore, sin b sin c sin A sin В sin С (51) sin a sin b sin c This equality indicates that: In a spherical triangle the sines of the angles are proportional to the sines of the opposite sides. EXERCISE XL VI 1. Derive the Sine formula geometrically, by dropping a perpendicular... | |
| |
In Every Spherical Triangle, the Sines of the Angles are Proportional to the Sines of their. Opposite Sides. If, from the first of the equations marked... 
