 | 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 - 642 pages
...value of c, having given A = 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,... | |
 | De Volson Wood - 1887 - 264 pages
...B' V с '-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)... | |
 | Webster Wells - Trigonometry - 1887 - 202 pages
...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 - 150 pages
...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... | |
 | Bennett Hooper Brough - Mine surveying - 1888 - 366 pages
...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... | |
 | Edwin Pliny Seaver - Trigonometry - 1889 - 306 pages
...a = 2 R sin AI b =2 R sin B \ ........ [117] с =2 Л sin С i 179. The sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite anyles is to the tangent of half their difference. ANALYTIC PROOF. The first two equations... | |
 | 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... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 196 pages
...provided the right order is maintained. 57. Law of Tangents. — 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. 55, a : b = sin A : sin B. By composition... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...provided the right order is maintained. 97. Law of Tangents. — 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. 95, a : b = sin A : sin B. By composition... | |
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C' (89) (90) (91) (92) (93) 112. 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. 
