 | 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
...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 - 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... | |
 | 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° -... | |
 | 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 to half their sum... | |
 | Edwin Pliny Seaver - Trigonometry - 1889 - 306 pages
...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... | |
 | Education - 1892 - 754 pages
...solving triangles ? 2. Prove: — In any plane triangle, the sum of the sides including either 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. 3. Find the sine of half an angle in terms... | |
 | 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... | |
 | 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... | |
 | Alfred Hix Welsh - Plane trigonometry - 1894 - 230 pages
...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... | |
| |
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. 
