| 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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