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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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