| James Morford Taylor - 1905 - 234 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 half their difference. From the law of sines, we have By... | |
| 1906 - 188 sider
...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... | |
| International Correspondence Schools - 1906
...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... | |
| Fletcher Durell - 1910 - 184 sider
...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... | |
| FLETCHER DURELL - 1911
...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... | |
| Robert Edouard Moritz - 1913 - 453 sider
...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... | |
| Charles Sumner Slichter - 1914 - 490 sider
...- C) c + a tan KC + A) c - a tan i(C - A) 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. GEOMETRICAL PROOP: From any vertex of the triangle... | |
| CLAUDE IRWIN PALMER - 1914
...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 = - —... | |
| Claude Irwin Palmer, Charles Wilbur Leigh - 1916 - 188 sider
...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.... | |
| William Charles Brenke - 1917 - 160 sider
...twice their product by the cosine of their included angle. Law of Tangents. — 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 difference. Half Angles. — The sine of half an angle... | |
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