Books Books 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. The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 81
by Peter Nicholson - 1823 - 596 pages ## Plane Trigonometry with Tables

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

Claude Irwin Palmer, Charles Wilbur Leigh - Logarithms - 1916 - 348 pages
...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.... ## Mathematics for Collegiate Students of Agriculture and General Science

Alfred Monroe Kenyon, William Vernon Lovitt - Mathematics - 1917 - 366 pages
...the third side when two sides and 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... ## Elements of Trigonometry: With Tables

William Charles Brenke - Trigonometry - 1917 - 200 pages
...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... ## Plane and Spherical Trigonometry

Leonard Magruder Passano - Trigonometry - 1918 - 330 pages
...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 = sin A... 