| 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,... | |
| De Volson Wood - 1887
...'-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 - 1887 - 103 sider
...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... | |
| Webster Wells - 1887 - 151 sider
...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... | |
| Bennett Hooper Brough - 1888 - 302 sider
...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 - 1889 - 284 sider
...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... | |
| Edward Albert Bowser - 1892 - 368 sider
...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... | |
| Edward Albert Bowser - 1892 - 172 sider
...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... | |
| Alfred Hix Welsh - 1894 - 206 sider
...CB - AB : : tan ^ (A + Cf) : tan £ (A - C). Hence, 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. Scholium. — The half difference added... | |
| Ephraim Miller - 1894 - 193 sider
...c. In like manner the others may be obtained. 64. THEORKM IV. In any triangle, the sum of two sides **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their differenve. From the fundamental formulae [31], sin... | |
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