Books Books In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 68
by Nathan Scholfield - 1845 - 232 pages ## Plane and Spherical Trigonometry

James Morford Taylor - Trigonometry - 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... ## Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - Building - 1906 - 620 pages
...formulas are derived in Appendix II. 20. Principle of Tangents. — 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. That is (Fig. 6), a + d _ ta a - b ~ tan... ## Plane Trigonometry

Plane trigonometry - 1906 - 230 pages
...formulas are derived in Appendix ll. 20. Principle of Tangents. — 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. That is (Fig. 6), ab tan i (A - B) The... ## Plane Trigonometry

Fletcher Durell - Plane trigonometry - 1910 - 348 pages
...collecting results, ab с sin C' sn . sin В 107 TRIGONOMETRY 75. Law of Tangents in a triangle. In any triangle the sum of any two sides is to their difference...the tangent of half the sum of the angles opposite the given sides is to the tangent of half the difference of these angles. In a triangle ABC (Figs.... ## Logarithmic and Trigonometric Tables

Fletcher Durell - Logarithms - 1911 - 336 pages
...collecting results, a 1} c sin A sin B 107 sin C' TRIGONOMETRY 75. Law of Tangents in a triangle. In any triangle the sum of any two sides is to their difference...the tangent of half the sum of the angles opposite the given sides is to the tangent of half the difference of these angles. In a triangle ABC (Figs.... ## Plane and Sperical Trigonometry (with Five-place Tables): A Text-book for ...

Robert Édouard Moritz - Trigonometry - 1913 - 560 pages
...(ü + Л) c- a tan 5 (С - Л) Formulas (7) embody the Law of tangents: In any triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite is to the tangent of half their difference. The formulas (6), which we shall have occasion to use hereafter,... ## Plane Trigonometry with Tables

Claude Irwin Palmer, Charles Wilbur Leigh - Plane trigonometry - 1914 - 308 pages
...Second method. — For a solution by logarithms the following theorem is needed: TANGENT THEOREM. 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. „ „ a sin a: f . ,, Proof. T = - —... ## Elementary Mathematical Analysis: A Text Book for First Year College Students

Charles Sumner Slichter - Functions - 1914 - 516 pages
..._ b - c ~ tan i(B - C) (t)> _ _ _ ca~tani(CA) (l)) Expressed in words: In any triangle, the sum of two sides is to their difference, as the tangent of half the sum of the angles opposite is to the tangent of half of their difference. GEOMETR1CAL PBOOF: From any vertex of the triangle as... ## Plane and Spherical Trigonometry

Claude Irwin Palmer, Charles Wilbur Leigh - Logarithms - 1916 - 348 pages
...Second method. — For a solution by logarithms the following theorem is needed: TANGENT THEOREM. 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. a sina Proof. r = -. — -, from sine theorem.... 