Books Books C' (89) (90) (91) (92) (93) 112. 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. The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 81
by Peter Nicholson - 1823 - 596 pages ## Annual Report

Public schools - 1878 - 716 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 circular... ## A New Treatise on Surveying and Navigation, Theoretical and Practical: With ...

Horatio Nelson Robinson - Navigation - 1878 - 564 pages
...without a circle, by Cor. Th. 18, B. Ill, we have AE x AF= AB x AG 89 PROPOSITION VII. The sum of any two sides of a triangle is to their difference, as the tangent of one half the sum of the angles opposite to these sides, is to the tangent of one half their difference.... ## The Elements of Plane and Spherical Trigonometry

Eugene Lamb Richards - Trigonometry - 1879 - 232 pages
...since C is a right angle, its sine is 1 (Art. 35). Also 49. In any 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. Let ACB be any triangle. Then BC+CA _ tan.... ## The Civil-engineer & Surveyor's Manual

Michael McDermott - Civil engineering - 1879 - 560 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. J (A... ## New American Practical Navigator

Nautical astronomy - 1880 - 884 pages
...triangle (supposing an;/ side to be the base, and calling the other two the sides, the sum of the sides is to their difference as the. tangent of half the sum of the angles at tht base is to the tangent of half the difference of the same angles. Thus, in the triangle ABC, if... ## A Treatise on Trigonometry by Profs. Oliver, Wait and Jones

Cornell University. Department of Mathematics - 1881 - 122 pages
...negative direction from the origin used. Тнм. 2. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference : 106] ie, (a + b) : (a~b) = tan ¿(A... ## A Treatise on Trigonometry

James Edward Oliver - Trigonometry - 1881 - 120 pages
...negative direction from the origin used. Tнм. 2. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference : 106] ie, (a + b) : (a~&) = tan¿(A... ## Text book of military topography

William Hamilton Richards - Military topography - 1883 - 256 pages
...two sides and the contained angle are known, and the third side is required. 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. Let the known sides be / 1076-53 and e 2846-39, and B the... ## A Practical Text-book on Plane and Spherical Trigonometry

Webster Wells - 1883 - 298 pages
...c = sin A : sтБ : sin С abc or, sin A sin Б sin Q 145. In any 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 Art. 144, a : b = sin Л : sin B Whence,... 