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" In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... "
Elementary text-book of trigonometry - Side 118
av Robert Hamilton Pinkerton - 1884 - 176 sider
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1886
...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°...
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Academic Trigonometry: Plane and Spherical

Thomas Marcus Blakslee - 1888 - 35 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...
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A Treatise on Plane Trigonometry, Containing an Account of Hyperbolic ...

John Casey - 1888 - 276 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:...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 1889
...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...
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Elementary Trigonometry

John Maximilian Dyer - 1891 - 266 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,...
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A Treatise on Plane Trigonometry

Ernest William Hobson - 1891 - 356 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,...
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Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - 1892 - 172 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) .-....
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An Elementary Treatise on Plane Trigonometry

Ernest William Hobson, Charles Minshall Jessop - 1892 - 324 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...
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A Treatise on Plane and Spherical Trigonometry: And Its Applications to ...

Edward Albert Bowser - 1892 - 368 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...
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Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - 1894 - 172 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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