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" 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. "
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811
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Trigonometry, Analytical, Plane and Spherical, with Logarithmic Tables

De Volson Wood - 1887 - 272 pages
...'-ftThis reduced by (66) gives __ 0-6 tan | (1-5)' that is, The sum of two sides of a plane triangle is to their difference, as the tangent of half the sum of the angles opposite is to the tangent of half their difference. Toßnd A + Б we "have A + Б = 180°...
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The Essentials of Plane and Spherical Trigonometry

Webster Wells - 1887 - 200 pages
...expressed more compactly as follows : , sin Л sin B sin (' 114. 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. Formula (45) of Art. 113 may be put...
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Plane Trigonometry

Webster Wells - 1887 - 158 pages
...more compactly as follows: ab с sin , I sin Б sin С 114. 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. Formula (45) of Art. 113 may be put...
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A Treatise on Mine-surveying

Bennett Hooper Brough - 1888 - 366 pages
...is required to find the two other angles, and the third side. In this case, the sum of the two sides is to their difference, as the tangent of half the sum of the two unknown angles is to the tangent of half their difference. Half their difference thus found,...
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Elementary Trigonometry, Plane and Spherical

Edwin Pliny Seaver - 1889 - 306 pages
...sin AI b =2 R sin B \ ........ [117] с =2 Л sin С i 179. The sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite anyles is to the tangent of half their difference. ANALYTIC PROOF. The first two equations...
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Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - 1892 - 194 pages
...provided the right order is maintained. 57. Law of Tangents. — 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. By Art. 55, a : b = sin A : sin B....
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A Treatise on Plane and Spherical Trigonometry: And Its Applications to ...

Edward Albert Bowser - 1892 - 392 pages
...provided the right order is maintained. 97. Law of Tangents. — 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. By Art. 95, a : b = sin A : sin B....
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Plane and Spherical Trigonometry

Alfred Hix Welsh - 1894 - 228 pages
...CB - AB : : tan ^ (A + Cf) : tan £ (A - C). Hence, 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. Scholium. — The half difference added...
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A Treatise on Plane and Spherical Trigonometry

Ephraim Miller - 1894 - 222 pages
...c. In like manner the others may be obtained. 64. THEORKM IV. In any triangle, 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 differenve. From the fundamental formulae [31],...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1895 - 450 pages
...£(A— B)— tang. |(A+B) . sin. A— sin. B~sin. |(A— B) cos. £(A+B)~ tang. £(A— B)' that is, The sum of the sines of two arcs or angles is to their difference os the tangent of half the sum of those arcs is to the tangent of half their difference. posite angles...
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