 | 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... | |
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