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 Livres Livres 31 - 40 sur 110 pour In any triangle, the sides are proportional to the sines of the opposite angles,....
In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C...
A Compleat Treatise of Practical Navigation Demonstrated from It's First ... - Page 57
de Archibald Patoun - 1734 - 414 pages
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Elementary Trigonometry

Henry Sinclair Hall, Samuel Ratcliffe Knight - 1893 - 404 pages
...tany tana + tanatan/3 = l. CHAPTER XIII. RELATIONS BETWEEN THE SIDES AND ANGLES OF A TRIANGLE. 137. In any triangle the sides are proportional to the sines of the opposite angles; that is, ab _ c sin A sin B sin G' (1) Let the triangle AEG be acute-angled. From...
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The Application of Graphic Methods to the Design of Structures

William Wade Fitzherbert Pullen - 1896 - 321 pages
...the triangle of forces XYZ, the angle the angle and the angle Z = C + D. XlC, And further, because in any triangle the sides are proportional to the sines of the opposite angles, then H Fs1 ~Y sin Z sin X and putting in the equivalents of the angles, we have HT?...
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Trigonometry for Beginners

John Bascombe Lock - 1896 - 147 pages
...Similarly it may be proved that, b = c cos A + a cos С ; c = а cos В + b cos A 106. III. 2"o proce that, in any triangle, the sides are proportional to the sines of the angles opposite; or, To proce that abc sin A sin В sin С From .4, any one of the angular points,...
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A Treatise on Refrigerating and Ice-making Machinery ...

1899
...or b : с — sm В : sIn С ; с sin С с - sin С а ~ sin A1 or с : а = sin С : sin Rule. — In any triangle, the sides are proportional to the sines of the opposite angles. Art. 615. RULES USED IN LOGARITHMS. RULES FOH THE CHARACTERISTIC. I. For a number...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

1899
...expressions for all the values of a, cosai (1 — Cos Í) = sin2!» (1 + cos <). 0) (2) 5. Prove that in any triangle the sides are proportional to the sines of the opposite angles. If in a triangle ABC perpendiculars are drawn from the vertices to the opposite sides,...
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Plane Trigonometry

Elmer Adelbert Lyman, Edwin Charles Goddard - 1899 - 91 pages
...(J. + B) a + b 52 i ¿i _ az III. Law of Cosines, cos A = — ?"— - , etc. ¿be 59. Law of Sines. In any triangle the sides are proportional to the sines of the angles opposite. Let ABO be any triangle, p the perpendicular from В on b. In I (Fig. 34), 0 is an...
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Plane and Spherical Trigonometry: An Elementary Text-book

Charles Hamilton Ashton, Walter Randall Marsh - 1900 - 157 pages
...considered. For the general form of these theorems and their proof, see Art. 43. 40. Law of the sines. — In any triangle, the sides are proportional to the sines of the opposite angles. In either Fig. 52 (a) or 52 (5), let the length of the perpendicular DO be represented...
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PLANE AND SPHERICAL TRIGONOMETRY

ELMER A. LYMAN - 1900
...( A + J9) a + b §2 i C2 _ a2 III. Law of Cosines, cosA = — ?-— - , etc. 2 be 59. Law of Sines. In any triangle the sides are proportional to the sines of the angles opposite. Let ABO be any triangle, p the perpendicular from B on b. In I (Fig. 34), C is an...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - 1901
...for all sizes of the angles A, B. Hence find all the trigonometrical ratios of 105°. 4. Prove that in any triangle the sides are proportional to the sines of the angles opposite to them ; and that the cosine of any angle of the triangle is expressible, in terms...
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Plane and Solid Analytic Geometry: An Elementary Textbook

Charles Hamilton Ashton - 1902 - 278 pages
...considered. For the general form of these theorems and their proof, see Art. 43. 40. Law of the sines. — In any triangle, the sides are proportional to the sines of the opposite angles. О h D -4 В FIG. Ы (Ь). In either Fig. 52 (a) or 52 (6), let the length of the...
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