 | 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 B. a : c = sin... | |
 | Dayton Clarence Miller - Physics - 1903 - 428 pages
...B, and C represent the three forces, and R the resultant of A and 5, which is equal to — C. In a triangle the sides are proportional to the sines of the opposite angles. It is evident that Fio. 22. TRIANOLE AND PARALLELOGRAM OF FORCES the angles a, b, and c are the supplements... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1904 - 453 pages
...sin2 x ; 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 the square of a... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1904 - 462 pages
...2 sin x 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 square of a side... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1905 - 240 pages
...П 1 • ] 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 any triangle the... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...marking and 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, be any triangle and... | |
 | Plane trigonometry - 1906 - 230 pages
...the sides and angles of a triangle, see Plane Trigonometry, Part 1. 18. Principle of Sines. — fn any triangle, the sides are proportional to the sines of the opposite angles. That is, a _ sin A a _ sin A b, _ sin B b sin B^ c sin C' c sin C Let ABC, Fig. 6, be any triangle... | |
 | 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 straight line... | |
 | 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 --:---- = ... ~ с. Sin В .... | |
 | William Charles Brenke - Algebra - 1910 - 374 pages
...to obtain. Additional relations will then be derived from these. The Law of Sines. — In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be the triangle, CD one of its altitudes. Two cases arise, according as D falls within or without... | |
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Law of Sines - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... 
