 | Education - 1883 - 748 pages
...finding the 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... | |
 | Webster Wells - Trigonometry - 1883 - 234 pages
...: a : b : с = sin A : sin В : sin С ab с sin A sin В sin O 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 A : sinB Whence,... | |
 | Education - 1883 - 642 pages
...finding the 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. 1. Before the Greeks,... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...principle, now to be demonstrated, viz. : In any plane triangle, the sum of the sides including any angle, is to their difference, as the tangent of half the sum of the two other angles, is to the tangent of half their difference. Let ABC represent any plane triangle,... | |
 | Great Britain. Education Department. Department of Science and Art - 1886 - 640 pages
...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,... | |
 | Webster Wells - Trigonometry - 1887 - 200 pages
...be expressed more compactly as follows : , sin Л sin B sin (' 114. 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. Formula (45) of Art. 113 may be put in... | |
 | Webster Wells - Plane trigonometry - 1887 - 158 pages
...expressed more compactly as follows: ab с sin , I sin Б sin С 114. 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. Formula (45) of Art. 113 may be put in... | |
 | De Volson Wood - 1887 - 272 pages
...'-ftThis reduced by (66) gives __ 0-6 tan | (1-5)' that is, The sum of two sides of a plane triangle is to their difference, as the tangent of half the sum of the angles opposite is to the tangent of half their difference. Toßnd A + Б we "have A + Б = 180° - G. (78)... | |
 | Bennett Hooper Brough - Mine surveying - 1888 - 366 pages
...known, and it is required to find the two other angles, and the third side. In this case, the sum of the two sides is to their difference, as the tangent of half the sum of the two unknown angles is to the tangent of half their difference. Half their difference thus found, added... | |
 | George William Usill - Surveying - 1889 - 306 pages
...opposite angle. B. In a plane triangle the sum of the sides is to their difference in the same ratio as the tangent of half the sum of the angles at the base of the triangle is to the tangent of half their difference. C. In a plane triangle the base is to 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... 
