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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 Surveying: Comprising the Theory and the Practice, Parte1

...are to each other at the opposite sides. THEOREM II.—In every plane triangle, the turn of two rides is to their difference as the tangent of half the sum of the angles opporite those sides is to the tangent of half their difference. THEOBBM HI.—In every plane...
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## Pamphlets in Philology and the Humanities, Volumen2

1897
...the sines of the opposite angles. That is, a : b = sin A : sin B The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles opposite is to the tangent of half their difference. That is, a -f J : a — I = tan £ ( A...
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## The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - 1902 - 1113 páginas
...formulas enable us to transform a sum or difference into a product. The sum of the sines of two angles is to their difference as the tangent of half the sum of those angles is to the tangent of half their difference. sin A + sin K _ 2 sin \^(A + B) cos J£C4...
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## The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - 1902 - 1129 páginas
...formulœ enable us to transform a sum or difference into a product. The sum of the sines of two angles is to their difference as the tangent of half the sum of those angles is to the tangent of half their difference. sin A + sin В 2 sin ЩА + B) cos WA - B)...
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## Plane Trigonometry

James Morford Taylor - 1904 - 171 páginas
...one of which is the law of tangents below. Law of tangents. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of their opposite angles is to the tangent of h (1ff their difference. From the law of sines, we have...
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## Plane and Spherical Trigonometry

Preston Albert Lambert - 1905 - 98 páginas
...B) Since a and b are any two sides of the triangle, in words the sum of any 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 the difference of these angles. The formula a -H1 _ tan £(A...
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## Plane and Spherical Trigonometry

James Morford Taylor - 1905 - 234 páginas
...one of which is the law of tangents below. Law of tangents. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of their opposite angles is to the tangent of half their difference. From the law of sines, we have By...
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## Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

...formulas are derived in Appendix II. 20. Principle of Tangents. — The sum of any 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. That is (Fig. 6), a + d _ ta a - b ~ tan...
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## Plane Trigonometry

1906 - 188 páginas
...formulas are derived in Appendix ll. 20. Principle of Tangents. — The sum of any 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. That is (Fig. 6), ab tan i (A - B) The...
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## Plane Trigonometry

Fletcher Durell - 1910 - 184 páginas
...sin В 107 TRIGONOMETRY 75. Law of Tangents in a triangle. In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the angles opposite the given sides is to the tangent of half the difference of these angles. In a triangle...
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