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" In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... "
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 68
by Nathan Scholfield - 1845 - 232 pages
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Pamphlets in Philology and the Humanities, Volume 2

English language - 1897 - 726 pages
...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 + B) : tan | ( A...
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A Treatise on Surveying, Comprising the Theory and the Practice, Volume 1

William Mitchell Gillespie - Surveying - 1897 - 610 pages
...to each other at the opposite sides. THEOREM II. — In every plane triangle, the sum of two tides is to their difference as the tangent of half the sum of the angles opposite those tides is to the tangent of half their difference. THEOREM III. — In every plane triangle, the...
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A Treatise on Surveying: Comprising the Theory and the Practice, Volume 1

William Mitchell Gillespie - Surveying - 1897 - 618 pages
...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 triangle,...
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The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - Engineering - 1907 - 1206 pages
...triangle — Theorem 1. The sines of the angles are proportional to the opposite sides. Theorem 2. 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. Theorem 3. If from any angle of a triangle...
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The Elements of Plane and Spherical Trigonometry

Thomas Ulvan Taylor, Charles Puryear - Trigonometry - 1902 - 242 pages
...42, C - 116, a = 564, to find ,4, b, c. 46. In Case 2 we need also The Law of Tangents. In any triangle, the sum of any two sides is to their difference as the tangent of one half the sum of the angles opposite those sides is to the tangent of one half their difference....
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The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - Engineering - 1902 - 1206 pages
...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 JC4...
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Ohio Educational Monthly and the National Teacher, Volume 52

Education - 1903 - 712 pages
...sin x , tan x of the fractions - and - as XX x approaches the limit o. 8. Demonstrate : — 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 the difference. GEOLOGY. i. Name the constituents of rocks....
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The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - Engineering - 1902 - 1224 pages
...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 - Plane trigonometry - 1904 - 192 pages
...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 - Trigonometry - 1905 - 120 pages
...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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