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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. "
A Treatise of Practical Surveying, ... - Página 94
por Robert Gibson - 1808 - 440 páginas
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A Treatise on Trigonometry

James Edward Oliver - 1881 - 102 páginas
...negative direction from the origin used. Tнм. 2. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference : 106] ie, (a + b) : (a~&) = tan¿(A + B)...
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The Ohio Educational Monthly and the National Teacher: A Journal ..., Volumen32

1883
...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. 2. What colonies were...
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A Practical Text-book on Plane and Spherical Trigonometry

Webster Wells - 1883
...c = sin A : sтБ : sin С abc or, sin A sin Б sin Q 145. 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. 144, a : b = sin Л : sin B Whence,...
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Text Book of Military Topography: Including the Courses of Instruction at ...

William Hamilton Richards - 1883 - 226 páginas
...two sides and the contained angle are known, and the third side is required. The sum of the two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let the known sides be / 1076-53 and e...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - 1885 - 512 páginas
...principle, now to be demonstrated, viz. : In any plane triangle, the sum of the sides including any 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. Let ABC represent any plane triangle, c and...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1886
...10°, a = 23087, b = 7903.2. (25.) 37. Prove geometrically that the sum of 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. In a triangle ABC, given a = 3, b = 5,...
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Trigonometry, Analytical, Plane and Spherical, with Logarithmic Tables

De Volson Wood - 1887
...'-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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Plane Trigonometry

Webster Wells - 1887 - 103 páginas
...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 in...
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The Essentials of Plane and Spherical Trigonometry

Webster Wells - 1887 - 151 páginas
...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...
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A Treatise on Mine-surveying

Bennett Hooper Brough - 1888 - 302 páginas
...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 to half their sum...
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