 | 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... | |
 | 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 are acute, as... | |
 | 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 given angles and... | |
 | 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
...; 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
...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
...• ] 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
...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... | |
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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... 
