| Ephraim Miller - Plane trigonometry - 1894 - 220 pages
...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 - Geometry - 1896 - 274 pages
...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 =... | |
| Webster Wells - Trigonometry - 1896 - 236 pages
...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... | |
| Charles Winthrop Crockett - Plane trigonometry - 1896 - 318 pages
...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... | |
| William Mitchell Gillespie - Surveying - 1896 - 594 pages
...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... | |
| William Mitchell Gillespie - Surveying - 1897 - 618 pages
...are to each other at the opposite sides. THEOREM II.—In every plane triangle, the turn of two rides **is to their difference as the tangent of half the sum of the** angles opporite those sides is to the tangent of half their difference. THEOBBM HI.—In every plane... | |
| English language - 1897 - 726 pages
...the sines of the opposite angles. That is, a : b = sin A : sin B The sum of two sides of a triangle **is to their difference as the tangent of half the sum of the** angles opposite is to the tangent of half their difference. That is, a -f J : a — I = tan £ ( A... | |
| William Kent - Engineering - 1902 - 1206 pages
...formulas enable us to transform a sum or difference into a product. The sum of the sines of two angles **is to their difference as the tangent of half the sum of** those angles is to the tangent of half their difference. sin A + sin K _ 2 sin \^(A + B) cos J£C4... | |
| James Morford Taylor - Plane trigonometry - 1904 - 192 pages
...one of which is the law of tangents below. Law of tangents. The sum of any two sides of a triangle **is to their difference as the tangent of half the sum of** their opposite angles is to the tangent of h (1ff their difference. From the law of sines, we have... | |
| William Kent - Engineering - 1902 - 1224 pages
...formulœ enable us to transform a sum or difference into a product. The sum of the sines of two angles **is to their difference as the tangent of half the sum of** those angles is to the tangent of half their difference. sin A + sin В 2 sin ЩА + B) cos WA - B)... | |
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