 | Charles Hamilton Ashton, Walter Randall Marsh - 1900 - 184 sider
...considered. For the general form of these theorems and their proof, see Art. 43. 40. Law of the sines. — In any triangle, the sides are proportional to the sines of the opposite angles. In either Fig. 52 (a) or 52 (5), let the length of the perpendicular DO be represented by h. Then in... | |
 | Elmer Adelbert Lyman - 1900 - 218 sider
...( A + J9) a + b §2 i C2 _ a2 III. Law of Cosines, cosA = — ?-— - , etc. 2 be 59. Law of Sines. In any triangle the sides are proportional to the sines of the angles opposite. Let ABO be any triangle, p the perpendicular from B on b. In I (Fig. 34), C is an... | |
 | Eldred John Brooksmith - 1901 - 368 sider
...for all sizes of the angles A, B. Hence find all the trigonometrical ratios of 105°. 4. Prove that in any triangle the sides are proportional to the sines of the angles opposite to them ; and that the cosine of any angle of the triangle is expressible, in terms... | |
 | International Correspondence Schools - 1902 - 794 sider
...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... | |
 | Arnold Lupton - 1902 - 494 sider
...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... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - 1902 - 186 sider
...considered. For the general form of these theorems and their proof, see Art. 43. 40. Law of the sines. — In any triangle, the sides are proportional to the sines of the opposite angles. О h D -4 В FIG. Ы (Ь). In either Fig. 52 (a) or 52 (6), let the length of the perpendicular DC... | |
 | Thomas Ulvan Taylor, Charles Puryear - 1902 - 242 sider
...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... | |
 | Dayton Clarence Miller - 1903 - 428 sider
...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 - 1904 - 453 sider
...; 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 - 1904 - 462 sider
...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... | |
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In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... 
