| Isaac Todhunter - 1868 - 200 sider
...oblique-angled triangles as well as for acute-angled triangles. We retain the notation of Art. 37. 104. **In any triangle the sides are proportional to the sines of the opposite angles. Let ABC be** a triangle, and from A draw AD perpendicular to the opposite side, meeting that side, or that side... | |
| Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 sider
...TRIANGLES. hence, b sm B _ ,, - == =: = tang B or 6 = с tang B. с cos В 120. Theorem III. In every plane **triangle the sides are proportional to the sines of the opposite angles. Let** A and B be any two angles of the triangle ABC. Let fall the perpendicular CD from the vertex C on the... | |
| Benjamin Greenleaf - 1869 - 382 sider
...— , therefore b=p cot A, tan.B=-, P b=p tan A cot B = |- , p = b cot B. (87) (88) 111. In any plane **triangle, the sides are proportional to the sines of the opposite angles. Let ABC be any triangle,** in which the sides opposite the angles A, /)', C, respectively, are denoted by a, b, and e. From one... | |
| James Hamblin Smith - 1870 - 224 sider
...cos В = cos 90° = 0, and л a . cos В = 0, and we have c= 6 . cus/i. 175. To shew t/1at in every **triangle the sides are proportional to the sines of the opposite angles.** Fig. 1. Fig. 2. о а J> JB А с ъ Я Let A, B be any two angles of the triangle ABC, and as one... | |
| Boston (Mass.). School Committee - 1873
...EXAMINATION. I. Name and illustrate all the trigonometrical functions of an arc. II. Prove that in any plane **triangle the sides are proportional to the sines of the opposite angles.** III. Prove that in any plane triangle the sum of any two sides is to their difference as the tangent... | |
| Benjamin Greenleaf - 1876 - 170 sider
...(4), cot A = — , therefore b=p cot шB= p 1 = p tan j = b cot A (87) (88) ..111. -S» аяу plane **triangle, the sides are proportional to the sines of the opposite angles.** В Let A В C be any triangle, in which the sides opposite the angles A, В, G, respectively, are denoted... | |
| J. G - 1878 - 372 sider
...relations and the formulae expressing them which are applied to the solution of triangles. 26. To show that **in any triangle the sides are proportional to the sines of the opposite angles,** 27. To express the cosine of an angle of a triangle in terms of the sides. 28. In every triangle each... | |
| William Chauvenet - 1879 - 256 sider
...formulae from a direct consideration of the solid angle itself. 3. In a spherical triangle, the sines of **the sides are proportional to the sines of the opposite angles. Let ABC,** Fig. 1, be a spherical triangle, 0 the center of the sphere. The angles' of the triangle are the inclinations... | |
| Clement Mackrow - 1879
...an angle the circular measure of which is g. lx 180^30 6 » *•' PROPERTIES OF TRIANGLES. In every **triangle the sides are proportional to the sines of the opposite angles.** FIG. 48. FIG. 49. FIG. 50. AA CB «• CO Note. — The sides opposite the angles A, B, c respectively... | |
| Thomas Kimber - 1880
...that sin. 2 A is less than 2 sin. A. Find sin. A from the equation tan. A + sec. A = a. 12. Show that **in any triangle the sides are proportional to the sines of the opposite angles.** One angle of a triangle is 120°, and the sides which contain it are in the ratio of 4 to 1. Show that... | |
| |