 | Samuel Webber - Mathematics - 1808 - 466 pages
...three such parts, that an angle and its opposite aide shall be two of them „• tojind the rest. In any plane triangle, the sides are proportional to the sines of their opposite angles.* That is, As one side t Is to another side : : So is sin. angle opp. the former... | |
 | Nicolas Pike - Algebra - 1808 - 470 pages
...9-87G4-6 So is AC 126 2- 10031To BC 9*'S 1-97683 SECTION 1 1. Of oUiquc angular Trigonometry. In any triangle, the sides are proportional to. the sines of the opposite angles. When two angles of any triangle are given, their sum, being subtracted from 1 80°, leaves the third... | |
 | George Watson - Navigation - 1822 - 72 pages
...of the same arc in another circle, as the radius of circle one is to the radius of the other. 193. In any plane triangle, the sides are proportional to the sines of their opposite angles. 194. In any right-angled triangle, the square of the longest side is equal to... | |
 | Richard Wilson - Logarithms - 1831 - 372 pages
...cos — sin ß 2 ß _ tan a -ß SECTION III. ON THE SOLUTION OF PLANE TRIANGLES. 108. PROP. In any triangle the sides are proportional to the sines of the opposite angles. For let ABC be the triangle. Let the angles be denoted by A, B, C,. and the sides opposite to them... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...R = 1, this becomes simply b = c sin I! — c cosA. PROP. II. THEOR. THE sides of a plane triangle are proportional to the sines of the opposite angles. Let ABC be any triangle; a : b : : sinA : sin 15 ; a : c : : sin A : sinC ; and b : c : : sin I! : sinC. Draw... | |
 | Roswell Park - Best books - 1841 - 722 pages
...hypothenuse, as the cosine of the angle at the base, is to radius, or the sine of 90°. In an oblique angled triangle, the sides are proportional to the sines of the opposite angles : also, the sum of any two sides is to their difference, as the tangent of the half sum of the two... | |
 | Richard Abbatt - Spherical astronomy - 1841 - 234 pages
...=9.9995833. Then log 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... | |
 | James Bates Thomson - Plane trigonometry - 1844 - 148 pages
...triangles ACD, BCD, CD=r AC sin A=BC sinB; whence (Euc. VI. 16) AC : BC : : sin B sin A ; that is, in any plane triangle, the sides are proportional to the sines of the opposite angles. Hence, also, ^nr; = - — — . ,,, . , TT i 22. One of the most important problems in trigonometry,... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...R=l, this becomes simply 6 = c sin B = c cos A. PROP. II. THEOR. — The sides of a plane triangle are proportional to the sines of the opposite angles. Let ABC be any triangle; then a : 6 : : sin A : sin B; a : c :: sin A : sin C ; and 6 : c : : smB : sin C. Draw... | |
 | Nathaniel Bowditch - 1846 - 854 pages
...calculator, from the introduction of the demonstrations among the precepto for calculatiou. LVIII. In any plane triangle, the sides are proportional...sines of the opposite angles. Let ABC be the triangle ; produce the shorter side, AB, to v F, making AF equal to BC ; from В and F let fall the perpendiculars... | |
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In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... 
