 | Great Britain. Education Department. Department of Science and Art - 1886 - 640 pages
...to construct an angle of 15°, and find from the construction the sine of 15°. (20.) 36. Show that in any triangle the sides are proportional to the sines of the opposita angles. AB is a lino 2,000 feet long; B is due east of A; at B a distant point P bears 46°... | |
 | Thomas Marcus Blakslee - Trigonometry - 1888 - 56 pages
...1^, we haye the usual formulas for sin A + sin B and cos A + cos B. PLANE. Law of Sines. In any plane triangle, the sides are proportional to the sines of the opposite angles. A nnm is By definition of sine, asiaB=p = b siaA. .-.. a : b = sin A : sin-B. Law of Cosines. The square... | |
 | John Casey - Geometry - 1888 - 300 pages
...of the tower, the height of the spire is SECTION II. — OBLIQUE-ANGLED TRIANGLES. 113. In any plane triangle the sides are proportional to the sines of the opposite angles. This proposition has been already proved in § 36, Cor. В Ю The following is the proof usually given:... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...geometrical figure that sin — , when expressed in terms of sin A, has four values. 7. Prove that in a triangle the sides are proportional to the sines of the opposite angles. If, in a triangle ABC, acosA = bcosB, prove that the triangle is isosceles or right angled. 8. The... | |
 | John Maximilian Dyer - Plane trigonometry - 1891 - 306 pages
...In all cases the lengths of the sides opposite the angles A, B, C, are denoted by a, b, e. 128. I. In any triangle the sides are proportional to the sines of the opposite angles ; ie - — - = - — — = — — — . 1 l sт A sin В sin С Fig. 2. From one of the angular points,... | |
 | Ernest William Hobson - Exponential functions - 1891 - 380 pages
...) a /sin A = b/ sin В = c/sin С ............... (2). The equations (2) express the fact that, ira any triangle, the sides are proportional to the sines of the opposite angles. 120. The relations (2) may also be proved thus: — Draw the circle circumscribing the triangle ABC,... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 194 pages
...— — (г 7. tan2A = 2 ab V - a1' 8. sin3A = c2 S ab2 -a3 OBLIQUE TRIANGLES. 55. Law of Sines. — In any triangle the sides are proportional to the...sines of the opposite angles. Let ABC be any triangle. Draw CD perpendicular to AB. We have, then, in both figures CD = a sin В = b sin A. (Art. 54) .-.... | |
 | Ernest William Hobson, Charles Minshall Jessop - Plane trigonometry - 1892 - 328 pages
...its sine is I, determine cos ^- by means of the expression (/3) of the last question. 5. Show that in any triangle the sides are proportional to the sines of the opposite angles. 6. If a straight line be drawn bisecting the angle A of a triangle ABC to meet the opposite side in... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...according as the included angle <, or > -• 190. Law of Sines. — In any spherical triangle the sines of the sides are proportional to the sines of the opposite angles. Let ABC be a spherical triangle, O the centre of the sphere ; and let a, b, с denote the sides of the triangle... | |
 | Edward Albert Bowser - Trigonometry - 1894 - 206 pages
...or >-• OBLIQUE SPHERICAL TRIANGLES. 9O. Law of Sines. — In any spherical triangle the sines of the sides are proportional to the sines of the opposite angles. Let ABC be a spherical triangle, O the centre of the sphere ; and let a, b, с denote the sides of the triangle... | |
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In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... 
