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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. "
The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 81
by Peter Nicholson - 1823 - 596 pages
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...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,...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1886 - 642 pages
...value of c, having given A = 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 - 264 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. To▀nd A + Б we "have A + Б = 180░ - G. (78)...
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The Essentials of Plane and Spherical Trigonometry

Webster Wells - Trigonometry - 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...
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Plane Trigonometry

Webster Wells - Plane trigonometry - 1887 - 150 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 in...
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A Treatise on Mine-surveying

Bennett Hooper Brough - Mine surveying - 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 - Trigonometry - 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...
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Practical Surveying: A Text-book for Students Preparing for Examinations Or ...

George William Usill - Surveying - 1889 - 306 pages
...opposite angle. B. In a plane triangle the sum of the sides is to their difference in the same ratio as the tangent of half the sum of the angles at the base of the triangle is to the tangent of half their difference. C. In a plane triangle the base is to the...
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Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - Trigonometry - 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...
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A Treatise on Plane and Spherical Trigonometry: And Its Applications to ...

Edward Albert Bowser - Trigonometry - 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...
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