 | Claude Irwin Palmer, Charles Wilbur Leigh - 1914 - 308 σελίδες
...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 = - —... | |
 | Charles Sumner Slichter - 1914 - 520 σελίδες
...- 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... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - 1916 - 348 σελίδες
...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 - 194 σελίδες
...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... | |
 | Alfred Monroe Kenyon, William Vernon Lovitt - 1917 - 384 σελίδες
...sides arid the included angle are given. 101. 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 a... | |
 | Leonard Magruder Passano - 1918 - 176 σελίδες
...54. Case III may be solved by means of the theorem following : In any triangle the sum of two sides is to their difference as the tangent of half the sum of the angles opposite the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b... | |
 | Leonard Magruder Passano - 1918 - 330 σελίδες
...54. Case III may be solved by means of the theorem following : In any triangle the sum of two sides is to their difference as the tangent of half the sum of the angles opposite the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b... | |
 | 1888 - 66 σελίδες
...logarithm of a number having four places. 5. Show that 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. GENERAL HISTORY. 1. Before the Greeks,... | |
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C' (89) (90) (91) (92) (93) 112. 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. 
