| Charles Davies - Geometry - 1854 - 436 pages
...oppo• rile sides. 90. We also have (Art. 22), a + b : ab :: tan $(A + B) : ta.n$(A — B): tha| is, **the sum of any two sides is to their difference, as the tangent of half the sum of the** opposite angles to the tangent of half their difference. 91. In case of a right•angled triangle,... | |
| Allan Menzies - 1854 - 520 pages
...Suppose AC, CB, and angle C to be given, then rule is, — Sum of the two sides (containing given angle) **is to their difference as the tangent of half the sum of the angles** at the base is to the tangent of half their difference ; half the sum = ^ (180 — angle C), then having... | |
| Charles Davies - Navigation - 1854 - 446 pages
...AC :: sin G : sin B. THEOREM II. In any triangle, the sum of the two sides containing either *ngle, **is to their difference, as the tangent of half the sum of the** two oilier angles, to the tangent of half their difference. 22. Let ACS be a triangle: then will AB+AC... | |
| William Mitchell Gillespie - Surveying - 1855 - 436 pages
...angles are to each other as the opposite sides. THEOREM II. — In every plane triangle, the sum of **two sides is to their difference as the tangent of half the sum of the angles opposite** those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle, the... | |
| Charles Davies - Geometry - 1855 - 336 pages
...sin A : sin BTheorems.THEOREM IIIn any triangle, the sum of the two sides contain1ng either angle, **is to their difference, as the tangent of half the sum of the** two other angles, to the tangent of half their differenceLet ACB be a triangle: then will AB + AC:AB-AC::t1M)(C+£)... | |
| William Smyth - Navigation - 1855 - 236 pages
...tan — ~ ; lU —4 a proportion, which we may thus enunciate ; the sum of 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. Ex. 1. Let AC (fig. 30) be 52. 96 -yds,... | |
| Elias Loomis - Trigonometry - 1855 - 192 pages
...i(A+B) . sin. A-sin. B~sin. i(AB) cos. i(A+B)~tang. i(AB) ' that is, The sum of the sines of two arcs **is to their difference, as the tangent of half the sum of** those arcs is to the tangent of half their difference. Dividing formula (3) by (4), and considering... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
..."•' which gives a : 5 : : sin. A : sin. B. . . (2.) In the same way it may be shown that THEOREM II. **In any plane triangle, the sum of any two sides is...their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. By Theorem I., we have 5 : c : : sin. B... | |
| McGill University - 1865 - 334 pages
...latter formula, determine tan. 15°, first finding tan. 30°. 5. The sum of the two sides of a triangle **is to their difference as the tangent of half the sum of the** base angles is to the tangent of half the difference. 6. Prove that if A" be the number of seconds... | |
| Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...; or cos. (A+B) : cos. A+sin. B :: cos. A— sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) **In any plane triangle, the sum of any two sides is...their difference as the tangent of half the sum of the** ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)... | |
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