| Edwin Pliny Seaver - 1889 - 284 páginas
...sin AI b =2 R sin B \ ........ [117] с =2 Л sin С i 179. The sum of two sides of a plane triangle **is to their difference as the tangent of half the sum of the** opposite anyles is to the tangent of half their difference. ANALYTIC PROOF. The first two equations... | |
| 1892
...solving triangles ? 2. Prove: — In any plane triangle, the sum of the sides including either angle **is to their difference as the tangent of half the sum of the two** other angles is to the tangent of half their difference. 3. Find the sine of half an angle in terms... | |
| Edward Albert Bowser - 1892 - 368 páginas
...provided the right order is maintained. 97. Law of Tangents. — In any triangle the sum of any two sides **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. By Art. 95, a : b = sin A : sin B. By composition... | |
| Edward Albert Bowser - 1892 - 172 páginas
...provided the right order is maintained. 57. Law of Tangents. — In any triangle the sum of any two sides **is to their difference as the tangent of half the sum, of the** opposite angles is to the tangent of half their difference. By Art. 55, a : b = sin A : sin B. By composition... | |
| Alfred Hix Welsh - 1894 - 206 páginas
...CB - AB : : tan ^ (A + Cf) : tan £ (A - C). Hence, in any plane triangle, the sum of any two sides **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. Scholium. — The half difference added... | |
| Ephraim Miller - 1894 - 193 páginas
...c. In like manner the others may be obtained. 64. THEORKM IV. In any triangle, the sum of two sides **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their differenve. From the fundamental formulae [31], sin... | |
| William Chauvenet - 1896 - 368 páginas
...proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =... | |
| Charles Winthrop Crockett - 1896 - 295 páginas
...Two Sides and the Included Angle (b, c, a) . First Method. — The sum of any two sides of a triangle **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. For we have b _ sin ß с sin y By composition... | |
| Webster Wells - 1896 - 126 páginas
...B : sin C, (48) and с : a = sin С : sin A. (49) 108. /n a»?/ triangle, the sum of any two sides **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. By (47), a : b = sin A : sin B. Whence... | |
| William Mitchell Gillespie - 1896 - 676 páginas
...to each other as the opposite sides. THEOREM H. — In every plane triangle, the sum of two sides u **to their difference as the tangent of half the sum of the** angles opposite those sides is to the tangent of half their difference. TE1EOBEM III. — In every... | |
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