 | Public schools - 1878 - 716 pages
...comes to rest ? 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... | |
 | 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, the... | |
 | 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
...then also Sin. B 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 - 1880 - 456 pages
...supplement of ABC, their sines are equal, Art. 13. Therefore sin. ABC : sin. C : : AC : AB. THEOREM II. 54. In any plane triangle, the sum of any two sides is...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... | |
 | 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,... | |
 | James Edward Oliver - Trigonometry - 1881 - 120 pages
...negative, according as it is measured in a positive or negative direction from the origin used. Tнм. 2. In any plane triangle, the sum of any two sides is...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... | |
 | Cornell University. Department of Mathematics - 1881 - 122 pages
...negative, according as it is measured in a positive or negative direction from the origin used. Тнм. 2. In any plane triangle, the sum of any two sides is...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... | |
 | Education - 1883 - 748 pages
...of 45°. 4. Give directions for finding the logarithm of a number having four places. 5. Show that in any plane triangle the sum of any two sides is...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... | |
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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... 
