 | International Correspondence Schools - Arithmetic - 1902 - 794 pages
...two solutions are possible. 615. The solution of the triangle depends upon the following principle: In any triangle, the sides are proportional to the sines of the opposite angles. Thus, referring to Fig. 68, the following proportions are true: a : b = sin A : sin... | |
 | Thomas Ulvan Taylor, Charles Puryear - Trigonometry - 1902 - 242 pages
...sides and the angles. Formulas embodying such relations will now be established. 44. Law of Sines. In any triangle the sides are proportional to the sines of the opposite angles. Fid. 31 Proof. In the triangle ABC draw the perpendicular CT). Then, if all the angles... | |
 | Arnold Lupton - Coal mines and mining - 1902 - 494 pages
...lx"-71° 18' 40"= 50° 22' 53" Case 2. — To solve a triangle, having giren two angles and a side. In any triangle the sides are proportional to the sines of the opposite angles. mi a '' >'• Thus . — r = -s — ^ = - -=f sin A sin B sin C Let A and C be the... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1904 - 453 pages
...; tan 2 x = l - tan2x .X l— COSX X /1+COSX 16. юп-=±д| jeoB-=±-' 16. Theorem. Law of sines. In any triangle the sides are proportional to the sines of the opposite angles ; rt Ъ r that is, sin A sin В sin С 17. Theorem. Law of cosines. In any triangle... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1904 - 462 pages
...cos x ; cos 2 x = cos2 x — sin2 x ; tan 2 x = x /1 15. sin- = ± •%/16. Theorem. Law of sines. In any triangle the sides are proportional to the sines of the opposite angles ; abc that is, sin A sin Б sin С 17. Theorem. Law of cosines. In any triangle the... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1905 - 240 pages
...• ] ji j14. sin2x = 2 sinx cos x ; cos 2 ж = cos2x — sin2x ; tan2x = 16. Theorem. Law of sines. In any triangle the sides are proportional to the sines of the opposite angles; abc that is, - — r = ^-;; = ^-^sm A sin В sm С 17. Theorem. Law of cosines. In... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...naming the sides and angles of a triangle, see Plane Trigonometry, Part 1. 18. Principle of Sines. — In any triangle, the sides are proportional to the sines of the opposite angles. That is, a. _ sin A a _ sin A .b sin R b sin B1 c sin C' c sin C Let ABC, Fig. 6,... | |
 | Charles Samuel Jackson, Robert Moir Milne - Statics - 1907 - 408 pages
...Lami's theorem is the translation into a statical proposition of the trigonometrical proposition that in any triangle the sides are proportional to the sines of the opposite angles. c Resolving. — If ABC is any A and AA', BB' and CC' are drawn perpendicular on any... | |
 | A. P. W. Williamson - Nautical astronomy - 1909 - 410 pages
...opposite one of them to find the other parts. EXAMPLE I.— Given В = 67° 22' 49", & = 45, с = 39. In any triangle the sides are proportional to the sines of the opposite angles, that is — c- • т > L- /^ Sin С с b : с :: Sin В : Sin С, or --:---- = ...... | |
 | Ernest William Hobson - Exponential functions - 1911 - 432 pages
...—a cos В + b cos A ) a/sin A = 6/sin В = c/sin С (2). The equations (2) express the fact that, in any triangle, the sides are proportional to the sines of the opposite angles. 120. The relations (2) may also be proved thus : — Draw the circle circumscribing... | |
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In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C... 
