| 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,... | |
| 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 _... | |
| Eugene Lamb Richards - Trigonometry - 1879 - 232 pages
...AC Sin. 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.... | |
| Michael McDermott - Civil engineering - 1879 - 560 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... | |
| Elias Loomis - Geometry - 1880 - 452 pages
...equal, Art. 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 of the angles at... | |
| Nautical astronomy - 1880 - 884 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... | |
| Cornell University. Department of Mathematics - 1881 - 122 pages
...measured in a 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 - 142 pages
...measured in a positive or negative direction from the origin used. THM. 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 : (b + c) : (b ~ c) = tan |(B + c) :... | |
| 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...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 contained angle 150° 7',... | |
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