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" The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. "
A Practical Application of the Principles of Geometry to the Mensuration of ... - Page 105
de Jeremiah Day - 1815 - 96 pages
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The Essentials of Plane and Spherical Trigonometry

Webster Wells - 1887 - 202 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 in the form a : b =...
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Trigonometry, Analytical, Plane and Spherical, with Logarithmic Tables

De Volson Wood - 1887 - 262 pages
...B' V с '-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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A Treatise on Plane Trigonometry, Containing an Account of Hyperbolic ...

John Casey - 1888 - 300 pages
...2 cos J- (A + Б) sin J (A - B] с sin С 2 sin i С cos J С But cos i (,4 + В) = sin J С; 116. The sum of any two sides of a triangle is to their difference as tan half the sum of the opposite angles is to tan half the difference. BEM.— From (306) we get a...
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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, added...
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Elementary Trigonometry, Plane and Spherical

Edwin Pliny Seaver - 1889 - 306 pages
...a = 2 R 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 of [117]...
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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. By composition and division,...
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Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - 1892 - 196 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. By composition and division,...
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The Ohio Educational Monthly and the National Teacher: A Journal ..., Volume 41

1892 - 750 pages
...solving triangles ? 2. Prove: — In any plane triangle, the sum of the sides including either angle is to their difference as the tangent of half the sum of the two other angles is to the tangent of half their difference. 3. Find the sine of half an angle in terms...
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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 to the half sum...
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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], sin A _ si nB _ sin...
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