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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...
A Compleat Treatise of Practical Navigation Demonstrated from It's First ... - Page 57
de Archibald Patoun - 1734 - 414 pages
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## Elementary text-book of trigonometry

Robert Hamilton Pinkerton - 1884 - 176 pages
...tanC(tanB - tan A)2 + 8 = - ±^ - "- - n2 \ m 2m? 4n2 u = — — o" x — ^ + " + 8 = -8 + 8 = 0. 84. In any triangle the sides are proportional to the sines of the opposite angles. Let ABC be any triangle, and let a perpendicular AD be 30 D AD = ABsinABC; also AD...
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## A Treatise on Higher Trigonometry

John Bascombe Lock - 1884 - 208 pages
...as в is indefinitely diminished. 6. Expand log, (1 + x) in a series of powers of x. Prove that 7. In any triangle the sides are proportional to the sines of the angles opposite to them. Through the angular point С of a triangle ABС is drawn any line CMN on which...
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## Cambridge university examination papers

...Prove that . + cos A 003-5- = !, ' 2 Which sign of the root is to bo taken if A > 180° < 270'? 7. In any triangle the sides are proportional to the sines of the opposite angles. Prove that cos A cos В _ l fsin B sin A\ ab ~ с (sin A sin B) ' 8. Prove the formula...
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## A Treatise on Elementary Trigonometry

John Bascombe Lock - 1885 - 274 pages
...=bcoaC + ecosB. [For, cos B = cos 90° = 0.] Similarly it may be proved that, 238. III. To prove that, in any triangle, the sides are proportional to the sines of the opposite angles ; or, To prove abc that sin A sin B sin 0 From A, any one of the angular points, draw...
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## Examination Papers for Science Schools and Classes

...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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## Examinations Papers

1886
...+ cos A sin B. Find what this formula becomes when B is replaced by ii's complement. 3. Prove that in any triangle the sides are proportional to the sines of the opposite angles. Prove that , J2 sin C + i3 sin B _ be sin A b + c ~ a 4. Shew how to solve a triangle,...
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## Elementary Trigonometry

John Maximilian Dyer - 1891 - 266 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...
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## An Elementary Treatise on Plane Trigonometry

Ernest William Hobson, Charles Minshall Jessop - 1892 - 324 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...
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## Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - 1892 - 172 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...
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## A Treatise on Plane and Spherical Trigonometry: And Its Applications to ...

Edward Albert Bowser - 1892 - 368 pages
...following : 1. tan B = cot A + cos C. 2. sin2A = sin2B. W -o? OBLIQUE TRIANGLES. 95. 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...
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