| Great Britain. Education Department. Department of Science and Art - 1886 - 640 sider
...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 - 1888 - 56 sider
...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 - 1888 - 300 sider
...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 - 1889 - 356 sider
...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 - 1891 - 306 sider
...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 - 1891 - 380 sider
...) 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 - 1892 - 194 sider
...— — (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 - 1892 - 328 sider
...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 - 1892 - 392 sider
...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 - 1894 - 206 sider
...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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