Books Books 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. An Easy Introduction to the Mathematics: In which the Theory and Practice ... - Page 405
by Charles Butler - 1814 ## 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... ## 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... ## The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - Railroad engineering - 1908 - 388 pages
...any plane triangle, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. 4. In any plane triangle, as the cosine of half the difference of the angles at the... ## Plane Trigonometry

Fletcher Durell - Plane trigonometry - 1910 - 348 pages
...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 as 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... ## Logarithmic and Trigonometric Tables

Fletcher Durell - Logarithms - 1911 - 336 pages
...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 as 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... ## 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... ## Plane Trigonometry with Tables

Claude Irwin Palmer, Charles Wilbur Leigh - Plane trigonometry - 1914 - 308 pages
...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... ## Plane and Spherical Trigonometry

Claude Irwin Palmer, Charles Wilbur Leigh - Logarithms - 1916 - 348 pages
...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.... 