 | Henry Sinclair Hall, Samuel Ratcliffe Knight - 1893 - 434 σελίδες
...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... | |
 | John Bascombe Lock - 1896 - 244 σελίδες
...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,... | |
 | William Wade Fitzherbert Pullen - 1896 - 344 σελίδες
...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?... | |
 | 1899 - 824 σελίδες
...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,... | |
 | Elmer Adelbert Lyman, Edwin Charles Goddard - 1899 - 188 σελίδες
...(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... | |
 | 1899 - 120 σελίδες
...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... | |
 | Elmer Adelbert Lyman - 1900 - 218 σελίδες
...( 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... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - 1900 - 184 σελίδες
...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... | |
 | Eldred John Brooksmith - 1901 - 368 σελίδες
...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... | |
 | Thomas Ulvan Taylor, Charles Puryear - 1902 - 242 σελίδες
...sides and the angles. Formulas embodying such relations will now be established. 44. Law of Sines. In any triangle the sides are proportional to the sines of the opposite angles. Fid. 31 Proof. In the triangle ABC draw the perpendicular CT). Then, if all the angles... | |
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In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C... 
