 | Charles Astor Bristed - 1852 - 470 pages
...(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... | |
 | War office - 1861 - 714 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... | |
 | Thomas Kimber - 1865 - 302 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... | |
 | James M'Dowell - 1866 - 124 pages
...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.... | |
 | Isaac Todhunter - 1866 - 216 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... | |
 | J. G - 1878 - 408 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... | |
 | Thomas Kimber - 1880 - 176 pages
...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... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...+ 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... | |
 | John Bascombe Lock - 1882 - 378 pages
...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,... | |
 | Thomas Grenfell Vyvyan - 1882 - 150 pages
...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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In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C... 
