| 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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