| Peter Nicholson - Mathematics - 1825 - 1046 pages
...angle ; that is, double the sine of that angle measured in the circle ; therefore the sides of the triangle are to each other as the. sines of the opposite angles measured in the same circle, and consequently as the sines of the same angles measured in a circle... | |
| Richard Abbatt - Spherical astronomy - 1841 - 234 pages
...c=log a + 10— cos 6: from this c=760.129. (48.) The sides of a plane triangle are proportional to the sines of the opposite angles. Let ABC be a plane triangle (fig. 8.), and BD the perpendicular from B upon the side AC ; then by (470, BD=AB . sin A, also BD=BC... | |
| Dennis M'Curdy - Geometry - 1846 - 168 pages
...secant of one of them takes, may be given to the cosine, cotangent, or cosecant of the other. 2 Th. The sides of a plane triangle are to each other as the sines of the angles opposite to them. In right angled triangles this proposition is obvious: for if the subtense... | |
| William Hill (land surveyor.) - Railroad engineering - 1847 - 32 pages
...angle ; that is, double the sine of that angle measured in the circle ; therefore the sides of the triangle are to each other as the sines of the opposite angles measured in the same circle, and consequently as the sines of the same angles measured in the circle... | |
| Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...rfe-f-the angle i«c = 90°; as also bed-^-lhe side ac = 90°. The sines of the sides of a spherical triangle are to each other as the sines of the opposite angles. Let abc (fig. 1 14) be a spherical triangle, whose sphere has its centre in o, and unity for radius. If now... | |
| 1851 - 716 pages
...-f- the angle bac = 90° ; as also bed -j- the side ac = 90°. The sines of the sides of a spherical triangle are to each other as the sines of the opposite angles. Let abc (Jig. 1 14) be a spherical triangle, whose sphere has its centre in o, and unity for radius. If now... | |
| Queen's University of Belfast - Education, Higher - 1852 - 306 pages
...lines over rugged and uneven ground? 11. The fundamental proposition in plane trigonometry is that the sides of a plane triangle are to each other as the sines of their respective opposite angles; prove this, and state its application to land surveying. 12. Give... | |
| James Elliot - 1851 - 162 pages
...problem. The rules for both problems are expressed by the following THEOREM : — The Sides of any Plane Triangle are to each other as the Sines of the opposite Angles. NOTE. Since, by the rule, we find the sine of the required angle, and not the angle itself, and since... | |
| W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...BD : : sine D : sine A ; and therefore, also, BA AD : : sine D : sine B. The above proposition, that the sides of a plane triangle are to each other as the sines- of the opposite angles is a fundamental one in trigonometry, and on it are based all the former observations that have been... | |
| Johann Georg Heck - Encyclopedias and dictionaries - 1860 - 332 pages
...de-|-the angle foze — 90 0 ; as also bed-\-i\\z side ac = 90°. The sines of the sides of a spherical triangle are to each other as the sines of the opposite angles. Let abc (fig. 114) be a spherical triangle, whose sphere has its centre in o, and unity for radius. If now... | |
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