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Livres Livres 11 - 20 sur 107 pour In any triangle, the sides are proportional to the sines of the opposite angles,....
" In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C... "
A Compleat Treatise of Practical Navigation Demonstrated from It's First ... - Page 57
de Archibald Patoun - 1734 - 414 pages
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Five Years in an English University, Volume 2

Charles Astor Bristed - 1852
...(45° + B ) = tan (45° — B) + 2 tan 2 B. cot 3 6 — cot d _ I ' ' cot 3 t + cot i ~ ~2cos20' 4. In any triangle the sides are proportional to the sines of the angles opposite to them. Also prove that sin A = ~ VS.(S — a)(S — b)(S — c). be 5. Given two...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 pages
...tan 2 A v ' Sin 3 A — sin A (3) (Cos A + cos B)2 + (sin A + sin B)2 = 4 cos2i( A - B) 4. Prove that in any triangle the sides are proportional to the sines of the opposite angles. 6. The angular elevation of the top of a tower is observed to be 60° 14'; the observer...
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A mathematical course for the University of London. (2nd)

Thomas Kimber - 1865 - 192 pages
...Show that cos. (A — В) = cos. A cos. В + sin. A sin. B. Find the cosine of 15°. 12. Show that in any triangle the sides are proportional to the sines of the opposite angles. Hence, deduce the expression for the cosine of an angle of a triangle in terms of...
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Trigonometry

James McDowell - 1866
...definition, ta.nA = cotB = T. o tanB = cotA = -; .-. a = b tanA = b cot-B, b = a tan.B= a cot A. 52. In any triangle the sides are proportional to the sines of the opposite angles. (4) (2) a Let ABC be any triangle, and from A draw AD perpendicular to BC or BC produced....
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Trigonometry for Beginners: With Numerous Examples

Isaac Todhunter - 1866 - 192 pages
...oblique-angled triangles as well as for acute- angled triangles. We retain the notation of Art. 37. 104. In any triangle the sides are proportional to the sines of the opposite angles. Let ABO be a triangle, and from A draw AD perpendicular to the opposite side, meeting...
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 372 pages
...relations and the formulae expressing them which are applied to the solution of triangles. 26. To show that in any triangle the sides are proportional to the sines of the opposite angles, 27. To express the cosine of an angle of a triangle in terms of the sides. 28. In...
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London graduation mathematics, questions in arithmetic and algebra set from ...

Thomas Kimber - 1880
...that sin. 2 A is less than 2 sin. A. Find sin. A from the equation tan. A + sec. A = a. 12. Show that in any triangle the sides are proportional to the sines of the opposite angles. One angle of a triangle is 120°, and the sides which contain it are in the ratio...
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad - 1880
...+ sin 2B -f sin 2C = 4 sin A sin B si (2.) tan A + tan B + tan C = tan A tan B tan C. 7. Show that, in any triangle, the sides are proportional to the sines of the opposite angles. Having given a = 3795 yards, B = 73° 15' 15", C = 42° 18' 30", find, by help of...
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A treatise on elementary trigonometry. [With] Key, by H. Carr

John Bascombe Lock - 1882
...bcosC + c cos 5. [For, cos B = cos 90° = 0.] Similarly it may be proved that, 238. III. To prove that in any triangle, the sides are proportional to the sines of the opposite angles ; or, To prove abc that sin 4 sin B sin C ' From A, any one of the angular points,...
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Introduction to plane trigonometry

Thomas Grenfell Vyvyan - 1882
...sign and magnitude of a sin 0 + 2 sin ^ e , as 6 changes from 0 to 2r. sin 8 - 2 sin 31 7. Prove that in any triangle the sides are proportional to the sines of the opposite angles. If then C=60°. 8. Solve a triangle, having given two angles and a side. Given 4 =...
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