 | John Charles Snowball - 1837 - 322 pages
...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 pages
...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 pages
...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 pages
...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 pages
...= • 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 pages
...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 pages
...— 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 pages
...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 pages
...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... | |
 | John Whitelaw - 1924 - 642 pages
...Cos b — cot A x cot c cos c Cos csm A Oblique Spherical Triangles (Fig. 230). Rule of Shies. — 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.... | |
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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 1, the value of cos A be drawn, and substituted for it in the equation sin2 A = 1 — cos2 A, we shall... 
