| Education - 1883 - 642 pages
...of 45°. 4. Give directions for finding the logarithm of a number having four places. 5. Show that **in any plane triangle the sum of any two sides is...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,... | |
| Webster Wells - Trigonometry - 1883 - 234 pages
...more compactly as follows : 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,... | |
| William Hamilton Richards - Military topography - 1883 - 256 pages
...in which 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 2846-39,... | |
| 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,... | |
| De Volson Wood - Trigonometry - 1885 - 334 pages
...This reduced by (66) gives (A + B) . " that is, Tfe SMWI o/" two sides of a plane triangle is to thcir **difference, as the tangent of half the sum of the angles opposite** is to the tangent of half their difference. To find A + B we. have A + B = 180° - 0. (78) To find... | |
| Great Britain. Education Department. Department of Science and Art - 1886 - 642 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 - Plane trigonometry - 1887 - 150 pages
...The above results may be 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... | |
| Webster Wells - Trigonometry - 1887 - 200 pages
...A a The above results may be expressed more compactly as follows : , sin A sin B sin G 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 - 264 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) Toßnd... | |
| 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... | |
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