| 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... | |
| Alfred Hix Welsh - Plane trigonometry - 1894 - 230 pages
...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... | |
| Charles Winthrop Crockett - Plane trigonometry - 1896 - 318 pages
...10'.2. 100. Case IV. Given 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 Chauvenet - Geometry - 1896 - 274 pages
...The 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... | |
| 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 plnne triangle,... | |
| English language - 1897 - 726 pages
...triangle are proportional to 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 + B) :... | |
| 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 triangle,... | |
| Charles Hamilton Ashton, Walter Randall Marsh - Trigonometry - 1900 - 184 pages
...vertices, similar expressions may be found for the other sides. 42. Law of the tangents. — The sum of any **two sides of a triangle is to their difference as the tangent of** one-half of the sum of the opposite angles is to the tangent of onehalf their difference. From formula... | |
| 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... | |
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