| Surveying - 1878 - 508 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... | |
| Michael McDermott - Civil engineering - 1879 - 586 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... | |
| Eugene Lamb Richards - Trigonometry - 1879 - 300 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.... | |
| Nautical astronomy - 1880
...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... | |
| James Edward Oliver - Trigonometry - 1881 - 102 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)... | |
| Cornell University. Department of Mathematics - 1881
...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 +... | |
| William Hamilton Richards - Military maps - 1883 - 226 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... | |
| Webster Wells - 1883
...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
...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... | |
| Great Britain. Education Department. Department of Science and Art - 1886
...10°, a = 23087, b = 7903.2. (25.) 37. Prove geometrically that the sum of two sides of a triangle **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. In a triangle ABC, given a = 3, b = 5,... | |
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