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. A Treatise of Practical Surveying, ... - Side 94av Robert Gibson - 1808 - 440 siderUten tilgangsbegrensning - Om denne boken
| 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... | |
| 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,... | |
| William Hamilton Richards - 1883 - 226 sider
...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... | |
| Charles Davies, Adrien Marie Legendre - 1885 - 512 sider
...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, c and... | |
| 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° -... | |
| 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 to half their sum... | |
| 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... | |
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