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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 Theory and Practice of Surveying: Containing All the Instructions ... - Page 106
by Robert Gibson - 1811 - 508 pages
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 pages
...=2 tan 2 A. 5. In any triangle, calling one side the base, prove that the sum of the other two sides is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. 6. Observers on two ships a mile apart...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 490 pages
...^ (A — B) f(\7\ sin A — sin B ~ wt~i (A + B) ; ( ' that is, The sum of the sines of two angles is to their difference as the tangent of half the sum of the angles is to the tangent of half their difference, or as the cotangent of half their difference is...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 490 pages
...sin ^1 sin £ siu C7° (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. For, by (90), a : b : : sin A : sin B ;...
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Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - Navigation - 1862 - 393 pages
...AC . : sin C : sin B. THEOREM IL In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of tt1e two oif1er angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...a sin A sin B sin 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. For, by (90), a : b : : sin A : sin B;...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - Trigonometry - 1863 - 256 pages
...proposition is therefore general in its application.* 118. The »urn of any two side» of a plane triangle ie to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =»...
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Elements of Plane Trigonometry: And Their Application to the Measurement of ...

William Frothingham Bradbury - Plane trigonometry - 1864
...the first proportion in Theorem I. THEOREM III. 41. 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. Let ABC be a triangle ; then AB + BC:BC—...
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Calendar of the McGill University, Montreal

McGill University - 1865
...latter formula, determine tan. 15°, first finding tan. 30°. 5. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the base angles is to the tangent of half the difference. 6. Prove that if A" be the number of seconds...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 283 pages
...sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)...
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Navigation

James Pryde - Navigation - 1867 - 458 pages
...the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half difference being added,...
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