| William Mitchell Gillespie - 1896
...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,... | |
| Webster Wells - 1896 - 126 sider
...B : sin C, (48) and с : a = sin С : sin A. (49) 108. /n a»?/ 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 (47), a : b = sin A : sin B. Whence... | |
| Charles Winthrop Crockett - 1896 - 295 sider
...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 - 1896 - 368 sider
...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 - 1897
...are to each other at the opposite sides. THEOREM II.—In every plane triangle, the turn of two rides **is to their difference as the tangent of half the sum of the angles** opporite those sides is to the tangent of half their difference. THEOBBM HI.—In every plane triangle,... | |
| 1897
...the sines of the opposite angles. That is, a : b = sin A : sin B The sum of two sides of a triangle **is to their difference as the tangent of half the sum of the angles** opposite is to the tangent of half their difference. That is, a -f J : a — I = tan £ ( A + B) :... | |
| William Kent - 1902 - 1113 sider
...formulas enable us to transform a sum or difference into a product. The sum of the sines of two angles **is to their difference as the tangent of half the sum of** those angles is to the tangent of half their difference. sin A + sin K _ 2 sin \^(A + B) cos J£C4... | |
| William Kent - 1902 - 1129 sider
...formulœ enable us to transform a sum or difference into a product. The sum of the sines of two angles **is to their difference as the tangent of half the sum of** those angles is to the tangent of half their difference. sin A + sin В 2 sin ЩА + B) cos WA - B)... | |
| James Morford Taylor - 1904 - 171 sider
...one of which is the law of tangents below. Law of tangents. The sum of any two sides of a triangle **is to their difference as the tangent of half the sum of** their opposite angles is to the tangent of h (1ff their difference. From the law of sines, we have... | |
| Preston Albert Lambert - 1905 - 98 sider
...B) Since a and b are any two sides of the triangle, in words 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 the difference of these angles. The formula a -H1 _ tan £(A... | |
| |