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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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Documents of the Assembly of the State of New York, Volume 96,Numéro 2

New York (State). Legislature. Assembly - 1873 - 818 pages
...we have the principle. When two sides and their included angles are given : The sum of the two sides is to their difference as the tangent of half the sum of the other two angles is to. the tangent of half their difference. This young man also worked out a problem...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1874 - 498 pages
...have tl1e following principle : In any plane triangle, the sum of the sides including either angle, is to their difference, as the tangent of half the sum of the two other angles, is to the tangent of half their difference. The half sum of the angles may he found...
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Cornell University Register and Catalogue

Cornell University - 1875 - 1012 pages
...sin'.r=:2cosa;r — 1 = I — 2sinV. 4. Prove that in any plane triangle the sum of cither two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of hall' their difference. 5. Given two sides of a triangle equal to 99.3425 and...
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - 1875 - 276 pages
...£(Л + ß) : tan £(Л — B). Hence, In any plane triangle, the sum of the sides inchuling an angle is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their difference. We find from the proportion, the equation...
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Military Surveying and Field Sketching ...

William Hamilton Richards - 1875 - 216 pages
...from 180°, E + F = 180° 150° T — 29° 3'. and \ (E + F) = 14° 31' 30". The sum of the two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Ar. co. Log. (e + /) 3922'92 = 6'406347...
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Plane and Spherical Trigonometry

Henry Nathan Wheeler - 1876 - 218 pages
...the above to Fig. 42, we must remember that sin B is equal to the sine of its supplement CBP. § 72. The sum of any two sides of a triangle is to their...the tangent of half the sum of the opposite angles is to the tangent of half their difference. From [67] we get, by the theoiy of proportions, — 6-...
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The Elements of Plane Trigonometry

Henry Nathan Wheeler - 1876 - 128 pages
...SOLUTION OF OBLIQUE TRIANGLES. § 71. The sides of any triangle are proportional to the sines of § 72. The sum of any two sides of a triangle is to their...the tangent of half the sum of the opposite angles is to the tangent of half their difference . . 73 § 73. The square of any side of a triangle is equal...
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Plane and Spherical Trigonometry

Henry Nathan Wheeler - 1876 - 252 pages
...OBLIQUE TBIANGLEs. 1 71. The sides of any triangle are proportional to the sines of { 72. The surn of any two sides of a triangle is to their difference...the tangent of half the sum of the opposite angles Is to the tangent of half their difference . . 78 § 73. The square of any side of a triangle is equal...
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The Elements of Plane Trigonometry

Henry Nathan Wheeler - 1876 - 130 pages
...the above to Fig. 42, we must remember that sin B is equal to the sine of its supplement CBP. § 72. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of tlie opposite angles is to the tangent of half their difference. From [67] we get, by the theory of...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1876 - 204 pages
...sin Л -f- sin В _ cot|(X — B) . . * ' and by (14), that is, The sum of the sines of two angles is to their difference as the tangent of half the sum of the angles is to the tangent of half their difference, or as the cotangent of half their difference is...
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