 | Eugene Lamb Richards - Plane trigonometry - 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 _... | |
 | 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 triangle,... | |
 | Michael McDermott - Civil engineering - 1879 - 552 pages
...two Sida and 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... | |
 | Eugene Lamb Richards - Trigonometry - 1879 - 232 pages
...C~AB' For, 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.... | |
 | Nautical astronomy - 1880 - 880 pages
...any 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... | |
 | Elias Loomis - Conic sections - 1880 - 452 pages
...13. Therefore sin. ABC : sin. C : : AC : AB. THEOREM II. 54. 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. Let ABC be any triangle ; then will CB... | |
 | William Findlay Shunk - Railroad engineering - 1880 - 362 pages
...any plane trianf/le, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. 4. In any plane triangle, as the cosine of half ( the difference... | |
 | Cornell University. Department of Mathematics - 1881 - 120 pages
...positive or 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... | |
 | James Edward Oliver - Trigonometry - 1881 - 120 pages
...positive or 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... | |
 | William Hamilton Richards - Military topography - 1883 - 256 pages
...in which 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... | |
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In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... 
