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" The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. "
A Practical Application of the Principles of Geometry to the Mensuration of ... - Page 105
de Jeremiah Day - 1815 - 96 pages
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A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - 1851 - 416 pages
...THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making...
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Elements of Plane Trigonometry: With Its Application to Mensuration of ...

William Smyth - 1852 - 198 pages
...AC : : tang — - — - tang ; "•" /^ a proportion, which we may thus enunciate : the sum of tioo 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. parts. Subtracting the angle C 45° from 180°, and dividing...
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The Practical Model Calculator, for the Engineer, Mechanic, Machinist ...

Oliver Byrne - 1852 - 604 pages
...as BE : BD : : AE : DF ; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. The sum of the unknown angles is found, by taking the given angle from 180°. In the plane triangle...
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The Practical Model Calculator: For the Engineer, Mechanic, Machinist ...

Oliver Byrne - 1852 - 600 pages
...be as BE : BD :: AE : DF; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their differenceThe sum of the unknown angles is found, by taking the given angle from 180°In the plane...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852 - 268 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 = sin A : sin В whence,...
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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - 1852 - 396 pages
...equal to 55° 28' 12" ; to solve the triangle. 81. Tlieorem. The sum of two sides of a triangle is tto their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. [B. p. 13.] Proof. We have (fig. 1), a : b = sin. A : sin....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1852 - 436 pages
...AC :: sin 0 : sin jR THEOEEM II. In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will AJ3...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1886 - 338 pages
...C : sin B. Theorems. THEOREM 11. In any triangle, the sum of the two sides containing eithe1 angle, is to their difference, as the tangent of half the sum of (he t1eo other angles, to the tangent of half their di/ereMe. Let ACB be a triangle: then will With...
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Navigation

James Pryde - 1867 - 506 pages
...the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half difference being added,...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - 1867 - 474 pages
...sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)...
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