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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.
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811

## Report of twenty-one years' experience of the Dick bequest for elevating the ...

Allan Menzies - 1854 - 520 pages
...Suppose AC, CB, and angle C to be given, then rule is, — Sum of the two sides (containing given angle) is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference ; half the sum = ^ (180 — angle...

## Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 436 pages
...also have (Art. 22), a + b : ab :: tan \$(A + B) : ta.n\$(A — B): tha| is, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half their difference. 91. In case of a right•angled triangle,...

## Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - 1854 - 446 pages
...AC :: sin G : sin B. THEOREM II. In any triangle, the sum of the two sides containing either *ngle, is to their difference, as the tangent of half the sum of the two oilier angles, to the tangent of half their difference. 22. Let ACS be a triangle: then will...

## A Treatise on Land Surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1855 - 436 pages
...to each other as 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 every...

## Elements of Plane Trigonometry, Surveying and Navigation

William Smyth - 1855 - 234 pages
...tan — ~ ; lU —4 a proportion, which we may thus enunciate ; the sum of 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. Ex. 1. Let AC (fig. 30) be 52. 96 -yds,...

## Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - 1855 - 192 pages
...BC, or sin. A : sin. B :: BC : AC. THEOREM II. (50.) In any plane triangle, the sum of any tico 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...

## A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1856 - 478 pages
...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 every...

## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1856 - 460 pages
...(2.) In the same way it may be shown that THEOREM II. 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. By Theorem I., we have 5 : c : : sin....