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 Theory and Practice of Surveying: Containing All the Instructions ... - Page 106
by Robert Gibson - 1811 - 508 pages ## A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

Surveying - 1878 - 534 pages
...to each other at the opposite sides. THEOREM IL—In every plane triangle, the sum of two tides it to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of kalf their difference. THEOKEJI III.—In every plane... ## 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... ## 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.... ## 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... ## 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 + B)... ## 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 +... ## 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... ## 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,... ## The Ohio Educational Monthly and the National Teacher: A Journal ..., Volume 32

Education - 1883 - 748 pages
...logarithm of a number having four places. 5. Show that 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. GENERAL HISTORY. 2. What colonies were... 