| Edwin Pliny Seaver - Trigonometry - 1889 - 306 pages
...sin AI b =2 R sin B \ ........ [117] с =2 Л sin С i 179. The sum of two sides of a plane triangle **is to their difference as the tangent of half the sum of the** opposite anyles is to the tangent of half their difference. ANALYTIC PROOF. The first two equations... | |
| Edward Albert Bowser - Trigonometry - 1894 - 206 pages
...since the naming of - — provided the right order is maintained, (l) 57. Law of Tangents. — In any **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 Art. 55, a : b = sin A : sin B. By composition... | |
| Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...sides makes no difference, provided the right order is maintained. 97. Law of Tangents. — In any **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 Art. 95, a : b = sin A : sin B. By composition... | |
| Education - 1892 - 754 pages
...solving triangles ? 2. Prove: — In any plane triangle, the sum of the sides including either angle **is to their difference as the tangent of half the sum of the** two other angles is to the tangent of half their difference. 3. Find the sine of half an angle in terms... | |
| Alfred Hix Welsh - Plane trigonometry - 1894 - 230 pages
...- C) . . . Art. 3, Def. 2. Л. jj .-. CB + AB : CB - AB : : tan ^ (A + Cf) : tan £ (A - C). Hence, **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. Scholium. — The half difference added... | |
| Ephraim Miller - Plane trigonometry - 1894 - 220 pages
...(3) by — c. In like manner the others may be obtained. 64. THEORKM IV. In any triangle, the sum of **two sides is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their differenve. From the fundamental formulae [31], sin... | |
| William Mitchell Gillespie - Surveying - 1896 - 594 pages
...to each other as the opposite sides. THEOREM H. — In every plane triangle, the sum of two sides u **to their difference as the tangent of half the sum of the angles opposite** those sides is to the tangent of half their difference. TE1EOBEM III. — In every plnne triangle,... | |
| Charles Winthrop Crockett - Plane trigonometry - 1896 - 318 pages
...Two Sides and the Included Angle (b, c, a) . First Method. — The sum of any 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. For we have b _ sin ß с sin y By composition... | |
| William Chauvenet - Geometry - 1896 - 274 pages
...proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle **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 the preceding article, a : b =... | |
| William Mitchell Gillespie - Surveying - 1897 - 592 pages
...angles are 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 eve.ry plane triangle,... | |
| |