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" THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles. "
The Elements of Plane and Spherical Trigonometry: And Its Application to ... - Page 31
by Richard Abbatt - 1841 - 191 pages
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 352 pages
...angles of a right-angled plane triangle is (Art. 13. and E. 32. 1.) the cosine of the other. (21.) The sides of a plane triangle are proportional to the sines of the angles opposite to them. For, if a circle be described (E. 5. 4.) about any plane triangle, the sides...
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Elements of Surveying: With the Necessary Tables

Charles Davies - Surveying - 1830 - 318 pages
...larger arc can enter into the calculations of the sides and angles of plane triangles. THEOREM. 43. The sides of a plane triangle are proportional to the sines of their opposite angles. Let ABC (PI. I. Fig. 2) be a triangle ; then, CB : CA : : sin. A : sin. B. For,...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...cosine of the adjacent' angle. When 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...
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Elements of Surveying: Including a Description of the Instruments and the ...

Charles Davies - Navigation - 1837 - 342 pages
...Ans. 28° 19' 4 5". We shall now demonstrate the principal theorems of Plane Trigonometry. THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles. 57. Let ABC be a triangle ; then will CB : CA : : sin A : sin B. For, with *#...
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - Surveying - 1839 - 376 pages
...Ans. 2 8° 19' 4 5". We shall now demonstrate the principal theorems of Plane Trigonometry. THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles. 57. Let ABC be a triangle ; then will CB : CA : : sin A : sin B. For, with A...
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - Surveying - 1839 - 376 pages
...Ans. 2 8° 19' 4 5". We shall now demonstrate the principal theorems of Plane Trigonometry. THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles. 57. Let ABC be a triangle ; then will CB : CA : : sin A : sin B. For, with A...
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Elements of Surveying, and Navigation: With a Description of the Instruments ...

Charles Davies - Navigation - 1841 - 414 pages
...Ans. 28° 19' 45". We shall now demonstrate the principal theorems of Plane Trigonometry. THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles. 57. Let ABC be a triangle ; then will CB : CA \: sin A : sin B. For, with A...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...cosine of the adjacent angle. When 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...
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The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 854 pages
...introduction of the demonstrations among the precepto for calculatiou. LVIII. In any plane triangle, the sides are proportional to the 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...
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Navigation and Nautical Astronomy: For the Use of British Seamen

James Inman - Nautical astronomy - 1849 - 302 pages
...hour in still water, and the current run at the rate of 3 miles an hour, AB : BC : : 6 : 3. But since the sides of a plane triangle are proportional to the sines of the opposite angles, AB : BC : : sin C : sin A ; where C is the angle between the bearing of D and the direction in which...
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