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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

## A Treatise on Plane and Spherical Trigonometry

Ephraim Miller - Plane trigonometry - 1894 - 220 pages
...c. In like manner the others may be obtained. 64. THEORKM IV. In any triangle, the sum of two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their differenve. From the fundamental formulae [31], sin...

## Plane and Spherical Trigonometry

Alfred Hix Welsh - Plane trigonometry - 1894 - 230 pages
...CB - AB : : tan ^ (A + Cf) : tan £ (A - C). Hence, 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. Scholium. — The half difference added...

## Elements of Plane and Spherical Trigonometry

Charles Winthrop Crockett - Plane trigonometry - 1896 - 318 pages
...10'.2. 100. Case IV. Given Two Sides and the Included Angle (b, c, a) . First Method. — 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. For we have b _ sin ß с sin y By composition...

## A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1896 - 274 pages
...The proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle 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 the preceding article, a : b =...

## New Plane and Spherical Trigonometry

Webster Wells - Trigonometry - 1896 - 236 pages
...B : sin C, (48) and с : a = sin С : sin A. (49) 108. /n a»?/ 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 (47), a : b = sin A : sin B. Whence...

## Treatise on Surveying

William Mitchell Gillespie - Surveying - 1896 - 594 pages
...to each other as the opposite sides. THEOREM H. — In every plane triangle, the sum of two sides u to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. TE1EOBEM III. — In every plnne triangle,...

## Pamphlets in Philology and the Humanities, Volume 2

English language - 1897 - 726 pages
...triangle are proportional to 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) :...

## 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,...