 | 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! :... | |
 | 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 :... | |
 | 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... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...28° 19' 45". 20. We shall now demonstrate the principal theorems of Plane Trigonometry. THEOEEM I. The sides of a plane triangle are proportional to the sines of their opposite angles. 21. Let ABC be a triangle ; then will CB : CA : : sin A : sin B. For, with A... | |
| |
CB : CA : : sin A : sin B. For, with A as a centre, and AD equal to the less side... 
