Books Books
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

## A Treatise on Surveying: Comprising the Theory and the Practice, Volume 1

William Mitchell Gillespie - Surveying - 1897 - 592 pages
...angles are to each other a& the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In eve.ry plane triangle,...

## 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) :...

## 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,...

## 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...

## The Elements of Plane and Spherical Trigonometry

Thomas Ulvan Taylor, Charles Puryear - Trigonometry - 1902 - 258 pages
...116°, a = 564, to find Л, f), 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....

## 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 J£C4...

## 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)...

## 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...