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" 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. "
An Easy Introduction to the Mathematics: In which the Theory and Practice ... - Page 405
by Charles Butler - 1814
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

Surveying - 1878 - 534 pages
...to each other at the opposite sides. THEOREM IL—In every plane triangle, the sum of two tides it to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of kalf their difference. THEOKEJI III.—In every plane triangle,...
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The Elements of Plane Trigonometry

Eugene Lamb Richards - Plane trigonometry - 1878 - 134 pages
...since C is a right angle, its sine is 1 (Art. 35). Also 49. In any triangle, the SUM of any TWO RIDES is to their DIFFERENCE as the TANGENT of HALF the sum of the OPPOSITE ANGLES 18 to the TANGENT of HALF their DIFFERENCE. Let A CB be any triangle. Then EC+CA _...
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The Elements of Plane and Spherical Trigonometry

Eugene Lamb Richards - Trigonometry - 1879 - 232 pages
...AC Sin. C~AB' For, since C is a right angle, its sine is 1 (Art. 35). Also 49. 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. Let ACB be any triangle. Then BC+CA _ tan....
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The Civil-engineer & Surveyor's Manual

Michael McDermott - Civil engineering - 1879 - 560 pages
...two Sida and their contained Angle given to Find the other Side and Angles. 203. Rule. The sum of the 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 -f Ъ : a — b : : tan. J (A...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1880 - 452 pages
...equal, Art. 13. Therefore sin. ABC : sin. C : : AC : AB. THEOREM II. 54. 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 any triangle ; then will CB...
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - Railroad engineering - 1880 - 362 pages
...any plane trianf/le, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. 4. In any plane triangle, as the cosine of half ( the difference of the angles at...
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New American Practical Navigator

Nautical astronomy - 1880 - 884 pages
...any triangle (supposing an;/ side to be the base, and calling the other two the sides, the sum of the sides is to their difference as the. tangent of half the sum of the angles at tht base is to the tangent of half the difference of the same angles. Thus, in the triangle ABC, if...
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A Treatise on Trigonometry by Profs. Oliver, Wait and Jones

Cornell University. Department of Mathematics - 1881 - 122 pages
...measured in a positive or negative direction from the origin used. Тнм. 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~b) = tan (A...
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A Treatise on Trigonometry

James Edward Oliver - Trigonometry - 1881 - 142 pages
...measured in a positive or negative direction from the origin used. THM. 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 : (b + c) : (b ~ c) = tan |(B + c) :...
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Text book of military topography

William Hamilton Richards - Military topography - 1883 - 256 pages
...in which 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...of the angles at the base, to the tangent of half their difference. Let the known sides be / 1076-53 and e 2846-39, and B the contained angle 150 7',...
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