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Books Books 1 - 10 of 90 on The sides of a triangle are proportional to the sines of the opposite angles..
" The sides of a triangle are proportional to the sines of the opposite angles. "
Elementary Synthetic Geometry of the Point, Line and Circle in the Plane - Page 183
by Nathan Fellowes Dupuis - 1889 - 294 pages
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...sides, angles, Sfc. of Triangles, or regular Poly* goni inscribed in, or circumscribed about it. (53.) THE sides of a triangle are proportional to the sines of the opposite angles. Let А, В, С be the angles, a, 6, с the sides opposite to them respectively of the triangle ABC....
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A Treatise on Algebra: Symbolical algebra and its applications to the ...

George Peacock - Algebra - 1845
...there is always i triangle of which they may form two of the angles. and it follows, therefore, that the sides of a triangle are proportional to the sines of the opposite angles. foronTs'ide *^8- The f>undamental equations in Art. 875, will readily of a triangle furnish us with...
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A Treatise on Algebra: Symbolical algebra and its applications to the ...

George Peacock - Algebra - 1845
...always " triangle of which they may form two of the angles. and it follows, therefore, that the tides of a triangle are proportional to the sines of the opposite angles. Expression 373. The fundamental equations in Art. 875, will readily for one side ' * of a triangle...
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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - Mathematics - 1846 - 468 pages
...we must investigate certain formulae connecting the parts of a triangle. 104 PLANE TRIGONOMETRY. 29. The sides of a triangle are proportional to the sines of the opposite angles. FIG. 1. FIG. 2. CD Let ABC be a triangle. From any angular point A let fall the perpendicular AD on...
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First book on plane trigonometry, comprising geometrical trigonometry

George Wirgman Hemming - 1851
...TRIANGLES. PAGE 51. When three parts of a triangle are given, it can generally be solved 83 52 — 53. The sides of a triangle are proportional to the sines of the opposite angles 84 54. To express the cosine of an angle of a triangle in terms of the sides 85 56. On the solution...
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A treatise on infinitesimal calculus, Volume 3

Bartholomew Price - 1856
...forces p, Q, R are proportional to the three lines OP, OQ, OR, or to OP, PR', R'OJ and since the three sides of a triangle are proportional to the sines of the opposite angles, therefore -J— = . Q = . R „ (29) sin OR' P sin a OP SIDOPE p QR or = = , sin a sin j3 sm y that...
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Parliamentary Papers, Volume 7

Great Britain. Parliament. House of Commons - Bills, Legislative - 1859
...as the arc varies through a circumference. 10. Prove that in a plane triangleĞa=6-+c2-26ccosA. 11. The sides of a triangle are proportional to the sines of the opposite angles. Prove this. 12. Investigate formula) for the solution of the different cases of plane triangles. 13....
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The Queen's [afterw.] Royal university of Ireland calendar

1859
...and less than four. Write the value of this ratio as far as five places of decimals. 17. Prove that the sides of a triangle are proportional to the sines of the opposite angles. 18. Given two sides and the included angle of a triangle, find the remaining side and angles. 19. Prove...
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An Introduction to Natural Philosophy: Designed as a Text- Book for the Use ...

Denison Olmsted, Ebenezer Strong Snell - Physics - 1860 - 456 pages
...component, it is not in the line of its action, because both forces act through the same point A. 46. Since the sides of a triangle are proportional to the sines of the opposite angles, these sines may also represent two components and their resultant. Thus, the sine of CAD corresponds...
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A mathematical course for the University of London. (2nd)

Thomas Kimber - Mathematics - 1865 - 192 pages
...(A — B), cos. (A + B), cos. (A — В). What is the numerical value of sin. 30° ? 7. Prove that the sides of a triangle are proportional to the sines of the opposite angles. (Oct. 27iA. — Rev. Prof. HEAVISIDE.) 8. Find by means of rectangular co-ordinates, the length of...
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