| 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... | |
| 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.... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
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