 | William Wade Fitzherbert Pullen - Graphic statics - 1896 - 344 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? 1 1? 1 ri • r<>... | |
 | John Bascombe Lock - Logarithms - 1896 - 244 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,... | |
 | Frederick Anderegg, Edward Drake Roe - Trigonometry - 1896 - 136 pages
...the angles opposite these sides by A, B, C, respectively. a. Theorem of Sines. § 65. In any plane triangle the sides are proportional to the sines of the opposite angles. Let ABC represent any plane triangle. Let p represent a perpendicular let fall from any vertex upon... | |
 | 1899 - 120 pages
...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 greater than 1 the... | |
 | Education - 1899 - 824 pages
...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, show that the... | |
 | Elmer Adelbert Lyman, Edwin Charles Goddard - Plane trigonometry - 1899 - 188 pages
...tan J (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... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - Trigonometry - 1900 - 184 pages
...angles. The letters a, b, and c simply represent the positive magnitudes of the sides, and A, E, and C the interior angles of the triangle. These forms of...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 by h. Then in... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...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 - Trigonometry - 1902 - 242 pages
...between the 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 are acute, as... | |
 | Arnold Lupton - Coal mines and mining - 1902 - 494 pages
...lx"-71° 18' 40"= 50° 22' 53" Case 2. — To solve a triangle, having giren two angles and a side. In any triangle the sides are proportional to the sines of the opposite angles. mi a '' >'• Thus . — r = -s — ^ = - -=f sin A sin B sin C Let A and C be the given angles and... | |
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Law of Sines - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... 
