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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
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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...
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - 1875 - 284 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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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...
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The Elements of Plane Trigonometry

Henry Nathan Wheeler - 1876 - 130 pages
...sides of any triangle are proportional to the sines of §72. 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 . . 73 § 73. The square of any side...
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Plane and Spherical Trigonometry

Henry Nathan Wheeler - 1876 - 254 pages
...sides of any triangle are proportional to the sines of { 72. The surn 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 . . 78 § 73. The square of any side...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - 458 pages
...|(A+B) cos. |(A— B)_tang. ~ "" sin. A— sin. B~sin. |(A— B) .cos. |(A+B)"~tang. i(A— B)' that is, The sum of the sines of two arcs or angles is to their...difference as the tangent of half the sum of those arcs is to the tangent of half their difference. Since the sides of a plane triangle arc as the sines of...
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Annual Report

1878 - 710 pages
...TRIGONOMETRY. Scientific Clatt. 1. Demonstrate, that in any plane triangle, the sure 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. 2. Give the limiting values of the...
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The Elements of Plane Trigonometry

Eugene Lamb Richards - 1878 - 134 pages
...since C is a right angle, its sine is 1 (Art. 35). Also 49. In any triangle, the SUM of any TWO RIDES is to their DIFFERENCE as the TANGENT of HALF the sum of the OPPOSITE ANGLES 18 to the TANGENT of HALF their DIFFERENCE. Let A CB be any triangle. Then EC+CA...
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The Civil-engineer & Surveyor's Manual

Michael McDermott - 1879 - 552 pages
...their contained Angle given to Find the other Side and Angles. 203. Rule. The sum of the 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 -f Ъ : a — b : : tan....
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