 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...B = —-, therefore b = p cot -4, p = b cot 5. 112. 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. For, by (90), a : 6 : : sin A : sin B;... | |
 | Charles Davies - Navigation - 1862 - 410 pages
...AC . : sin C : sin B. THEOREM IL In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of tt1e two oif1er angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...a sin A sin B sin C' (89) (90) (91) (92) (93) 112. 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. For, by (90), a : b : : sin A : sin B;... | |
 | William Chauvenet - Trigonometry - 1863 - 272 pages
...proposition is therefore general in its application.* 118. The »urn of any two side» of a plane triangle ie 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 =»... | |
 | William Frothingham Bradbury - Plane trigonometry - 1864 - 324 pages
...the first proportion in Theorem I. THEOREM III. 41. 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. Let ABC be a triangle ; then AB + BC:BC—... | |
 | McGill University - 1865 - 332 pages
...tan. B tan. (A + B) = ^b a. From the 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
...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.)... | |
 | James Pryde - Navigation - 1867 - 506 pages
...the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half difference being added,... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...± DA = BC-cos. C + BA-cos. A. That is, b = a cos. C -f- c cos. A. S6J). Theorem — The sum of any two sides of a triangle is to their difference as the tangent of half the sum •of the two opposite angles is to the tangent of half their difference. By Art. 867, a : b : : sin. A : sin.... | |
 | William Mitchell Gillespie - Surveying - 1868 - 530 pages
...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,... | |
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C' (89) (90) (91) (92) (93) 112. 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. 
