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" ... the side opposite the given angle is less than the other given side, the solution is impossible. "
Elements of Plane Trigonometry: With Its Application to Mensuration of ... - Page 21
by William Smyth - 1852 - 176 pages
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A Complete Epitome of Practical Navigation ...

John William Norie - Nautical astronomy - 1852 - 838 pages
...other given side, then the angle opposite that other given side, is always acute ; but when the given side, opposite the given angle, is less than the other given side, then the angle opposite that other given side may be either acute or obtuse, which consequently must...
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Elements of Plane Trigonometry, Surveying and Navigation

William Smyth - Navigation - 1855 - 234 pages
...triangle (fig. 14), 40 feet, the angle ABC 52°, and the angle BAC 70°, to find the remaining sides. 15. It is now evident, that we may always construct...the given angle is less than the other given side, in order to determine the triangle we must know whether the angle sought be acute or obtuse. 16. From...
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Elements of Plane Trigonometry: And Their Application to the Measurement of ...

William Frothingham Bradbury - Plane trigonometry - 1864 - 324 pages
...11' 2", comp. 0.404851 : sin. C 131° 4' 58" 9.877234 : : b 49.87 1.697839 : c 95.483 1.979924 If BC, the side opposite the given angle, is less than the other given side AC, and the given angle is ^^^V/ I \./ acute, there are two triangles which **''**-£-,-• B satisfy...
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A Treatise on Surveying: In which the Theory and Practice are Fully ...

Samuel Alsop - Surveying - 1865 - 440 pages
...should be taken acute or obtuse. By reference to the construction, (Fig. 46,) we see that whenever the side opposite the given angle is less than the other given side, and greater than the perpendicular BD, the triangle will admit of two forms: ABC, in which the angle...
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Trigonometry ...

James McDowell - 1866 - 124 pages
...than b, and therefore A may be either acute, right, or obtuse, but B must be acute. Therefore when the side opposite the given angle is less than the other given side, there are generally two solutions ; and when it is greater than the other side, there is only one solution....
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...angle A is less than the perpendicular, or if the given angle is right or obtuse, and at the same time the side opposite the given angle is less than the other given side, the solution is impossible. 131 Corollary. From this and the preceding Problem and Theorems VIII.,...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...angle A is less than the perpendicular, or if the given angle is right or obtuse, and at the same time the side opposite the given angle is less than the other given side, the solution is impossible. 13. Corollary. From this and the preceding Problem and Theorems VIII.,...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...either equal or one is the supplement of (he other. This Proposition follows from Problem 11, BV When the side opposite .the given angle is less than the other given side, we may construct two triangles, ABE, ABF, having two sides and an angle - of the one equal to two sides...
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The Elements of Plane Trigonometry

Eugene Lamb Richards - Plane trigonometry - 1878 - 134 pages
...formed. 56. To solve the triangle, when the parts are given as in the preceding article; that is, when the side opposite the given angle is less than the other given side, and greater than the product of the sine of the given angle by that side. Suppose we have given the...
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The Elements of Plane and Spherical Trigonometry

Eugene Lamb Richards - Trigonometry - 1879 - 232 pages
...formed. 56. To solve the triangle, when the parts are given as in the preceding article; that is, when the side opposite the given angle is less than the other given side, and greater than the product of the sine of the given angle by that side. Suppose we have given the...
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