| 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... | |
| 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,... | |
| 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... | |
| 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 *#... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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