 | Education - 1899 - 824 pages
...expressions for all the values of a, cosai (1 — Cos Í) = sin2!» (1 + cos <). 0) (2) 5. Prove that in any triangle the sides are proportional to the sines of the opposite angles. If in a triangle ABC perpendiculars are drawn from the vertices to the opposite sides, show that the... | |
 | 1899 - 120 pages
...с — sm В : sIn С ; с sin С с - sin С а ~ sin A1 or с : а = sin С : sin Rule. — In any triangle, the sides are proportional to the sines of the opposite angles. Art. 615. RULES USED IN LOGARITHMS. RULES FOH THE CHARACTERISTIC. I. For a number greater than 1 the... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - Trigonometry - 1900 - 184 pages
...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... | |
 | 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... | |
 | International Correspondence Schools - Arithmetic - 1902 - 794 pages
...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
...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... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - Trigonometry - 1902 - 186 pages
...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... | |
 | 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 - 462 pages
...14. sin2z = 2sinzcosz ; cos2z = cos2z — sin2z ; tan2z = l + COSZ 16. Theorem. Law of sines. In any triangle the sides are proportional to the sines of the opposite angles; Ь с 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 - 1904 - 462 pages
...; 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... 
