 | Webster Wells - 1896 - 236 pages
...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 - 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... | |
 | William Chauvenet - 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 :... | |
 | 1897 - 726 pages
...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 £... | |
 | William Mitchell Gillespie - 1897 - 618 pages
...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... | |
 | William Kent - 1902 - 1204 pages
...The sines of the angles are proportional to the opposite sides. Theorem 8. 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. Theorem 3. If from any angle of a triangle... | |
 | William Kent - 1902 - 1224 pages
...These 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) _ tan... | |
 | James Morford Taylor - 1904 - 192 pages
...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... | |
 | James Morford Taylor - 1905 - 256 pages
...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 half their difference. From the law of sines, we have By... | |
 | Preston Albert Lambert - 1905 - 120 pages
...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... | |
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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. 
