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" In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... "
Elementary text-book of trigonometry - Side 118
av Robert Hamilton Pinkerton - 1884 - 176 sider
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Trigonometry for beginners

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...
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Elements of Trigonometry, Plane and Spherical

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...
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Elements of Geometry and Trigonometry: With Practical Applications

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...
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Elementary Trigonometry

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...
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Annual Report of the School Committee of the City of Boston

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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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...
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First B.A. Examination, University of London: A Hand-book to the Study of ...

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...
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A Treatise on Plane and Spherical Trigonometry

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...
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The naval architect's and shipbuilder's pocket book of formulæ [&c.].

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...
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London graduation mathematics, questions in arithmetic and algebra set from ...

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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