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" In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... "
Elementary text-book of trigonometry - Side 118
av Robert Hamilton Pinkerton - 1884 - 176 sider
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 sider
...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 then retires...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 sider
...product of the other side into the cotangent of the angle. TRIGONOMETRY. (87) (88) 111. In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be any triangle, in which the sides opposite the angles A, B, C, respectively, are denoted by a, b, and c. From one...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1861 - 490 sider
...= — , ^ P b=p tan 7?. (87) therefore b = p cot «**=£, p = i cot 5. (88) 1 1 1 . /.< any /(fane triangle, the sides are proportional to the sines of the opposite angles. B Let ABG be any triangle, in which the sides opposite the angles A, B, C, respectively, are denoted...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 sider
...RELATIONS BETWEEN THE SIDES AND ANGLES OF SPHERICAL TRIANGLES. 148. In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. Let А В С be any spherical triangle ; А, Д and С the angles opposite to its sides a, b, and c, respectively;...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1863 - 320 sider
..., therefore b = p cot .4, -*=£, b = p tan B. cot B = ~- , p = b cot 5. (87) (88) 111. In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be any triangle, in which the sides opposite the angles A, B, C, respectively, are denoted by a, b, and c. From one...
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Plane Trigonometry for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - 1864 - 279 sider
...each side is equal to the product of the cotangent of the adjacent angle into the other side. 214. In any triangle the sides are proportional to the sines of the opposite angles. D Let ABC be any triangle, and from A draw AD perpendicular to the opposite side meeting that side,...
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A mathematical course for the University of London. (2nd)

Thomas Kimber - 1865 - 192 sider
...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 the sides. 13. Find...
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Plane trigonometry and logarithms

John Walmsley - 1865 - 182 sider
...a, b, с for the sides respectively opposite to them. 88. In any triangle the sides are respectively proportional to the sines of the opposite angles. Let ABC be any triangle. Draw CD perpendicular to AB, falling (1) within the triangle, and (2) without it. In (2) the angles...
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Trigonometry for beginners

Isaac Todhunter - 1866 - 192 sider
...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 that side, or that...
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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. From the...
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