In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. Documents of the City of Boston - Pàgina 139per Boston (Mass.). City Council - 1869Visualització completa - Sobre aquest llibre
| Allan Menzies - 1854 - 520 pàgines
...4. 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),... | |
| Charles Davies - 1854 - 446 pàgines
...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... | |
| Charles Davies - 1855 - 340 pàgines
...or BC : AC : : sin A : sin BTheorems.THEOREM IIIn any triangle, the sum of the two sides contain1ng either angle, is to their difference, as the tangent...the two other angles, to the tangent of half their differenceLet ACB be a triangle: then will AB + AC:AB-AC::t1M)(C+£) : tan %(CE)With A as a centre,... | |
| William Mitchell Gillespie - 1855 - 436 pàgines
...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... | |
| William Smyth - 1855 - 234 pàgines
...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 - 1855 - 192 pàgines
...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 - 1856 - 460 pàgines
...(2.) In the same way it may be shown that THEOREM II. 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. By Theorem I., we have 5 : c : : sin. B... | |
| Peter Nicholson - 1856 - 518 pàgines
...+ BC :: AC-BC : AD — BD. TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle 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. Let ABC be a triangle 4 then, of the... | |
| William Mitchell Gillespie - 1856 - 478 pàgines
...to each other a* 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... | |
| Adrien Marie Legendre, Charles Davies - 1857 - 442 pàgines
...comparing the sides AB, AC, in a similar manner, we should find, AB : AC :: sin C : sin B, THEOREM II. In any triangle, the sum of the two sides containing...other angles, to the tangent of half their difference. 22. Let A CB be a triangle : then will AB + AC : AB-AC : : tan %(C+B) : tan %(CB). With A as a centre,... | |
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