 | William Smyth - Navigation - 1855 - 234 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,... | |
 | Charles Davies - Geometry - 1855 - 340 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+£)... | |
 | 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... | |
 | William Mitchell Gillespie - Surveying - 1856 - 478 pages
...triangle, the sines of the angles are to each other a* the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference...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 cosine of... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...B. . . (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 - Cabinetwork - 1856 - 518 pages
...+ 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 two sides,... | |
 | William Mitchell Gillespie - Surveying - 1857 - 538 pages
...to each other at the opposite sides. THEOREM II.— In every plane triangle, the turn of two tides 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 cosine of... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...90. We also have (Art. 22), a + b : a - b : : tan %(A + B) : tan %(A - B) : that 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 thtir difference. 91. In case of a right•angled triangle,... | |
 | McGill University - 1865 - 332 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
...cos. A— sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides is to 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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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. 
