 | Great Britain. Education Department. Department of Science and Art - 1886 - 640 pages
...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...angles is to the tangent of half their difference. In a triangle ABC, given a = 3, b = 5, and C = 120°, find the tangent of (BA) — 2. . (25.) 38. AB... | |
 | Webster Wells - Plane trigonometry - 1887 - 158 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...angles is to the tangent of half their difference. Formula (45) of Art. 113 may be put in the form a: b = s\nA : sin B. Whence, by composition and division,... | |
 | Webster Wells - Trigonometry - 1887 - 200 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...angles is to the tangent of half their difference. Formula (45) of Art. 113 may be put in the form a : b = sin A. : sin />'. Whence, by composition and... | |
 | Edwin Schofield Crawley - Trigonometry - 1890 - 184 pages
.... ч (82) or PLANE TIUGONOMETKY. 62. In any triangle the sum of two sides is to their difference ae the tangent of half the sum of the opposite angles is to the tangent of half their difference. From (82), a_ _ sin A b sin B. By composition and division, But, by (64), a -\- b _ sin A -f• sin... | |
 | 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...angles is to the tangent of half their difference. By Art. 95, a : b = sin A : sin B. By composition and division, q + b __ sin A + sin B a — b sin... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 194 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...angles is to the tangent of half their difference. By Art. 55, a : b = sin A : sin B. By composition and division, a + b _ sin A 4- sin В a — b sin... | |
 | Alfred Hix Welsh - Plane trigonometry - 1894 - 228 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...angles is to the tangent of half their difference. Scholium. — The half difference added to the half sum gives the greater angle, and, subtracted from... | |
 | Ephraim Miller - Plane trigonometry - 1894 - 222 pages
...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...the opposite angles is to the tangent of half their differenve. From the fundamental formulae [31], sin A _ si nB _ sin C --a~ ~b~ "IP we obtain n .a +... | |
 | William Kent - Engineering - 1895 - 1234 pages
...proportional to the opposite slde^. Tkrtrrein У. The sum of any two sides la to their difference us the tangent of half the sum of the opposite angles is to the tangent of half their differ ence. Theorem Я. If from any angle of a triangle a perpendicular be drawn to the opposite side... | |
 | William Chauvenet - Geometry - 1896 - 274 pages
...Art. 39, it has the same ein*, so that the triangle OB P gives л the same as was found from Fig. 10. The proposition is therefore general in its application.*...composition and division, a + b : a — b = sin A + sin В : sin A — sin В But from (109) if x — А, у = В we obtain the proportion sin A + sin В :... | |
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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. 
