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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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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880
...+ sin 2B -f sin 2C = 4 sin A sin B si (2.) tan A + tan B + tan C = tan A tan B tan C. 7. Show that, in any triangle, the sides are proportional to the sines of the opposite angles. Having given a = 3795 yards, B = 73° 15' 15", C = 42° 18' 30", find, by help of logarithmic tables,...
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A Treatise on Trigonometry

James Edward Oliver - 1881 - 102 sider
...SOLUTION OF PLANE TRIANGLES. § 1. GENERAL PROPERTIES OF PLANE TRIANGLES. —^THEOREM 1. In any plane triangle the sides are proportional to the sines of the opposite angles. Let ABC be any triangle ; a, &, c the sides opposite the angles А, в, c respectively ; then will : 103] a:& = smA:sinB; b...
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A Treatise on Trigonometry by Profs. Oliver, Wait and Jones

Cornell University. Department of Mathematics - 1881
...SOLUTION OF PLANE TRIANGLES. § 1. GEKERAL PROPEETIES OF PLANE TRIANGLES. THEOREM 1 . In any plane triangle the sides are proportional to the sines of the opposite angles. Let ABC be any triangle ; a, b, с the sides opposite the angles А, в, с respectively ; then will : 103] ft : & = SÍHA:...
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A Treatise on Trigonometry

James Edward Oliver - 1881 - 102 sider
...SOLUTION OF PLANE TRIANGLES. § 1. GENERAL PROPERTIES OF PLANE TRIANGLES. THEOREM 1 . In any plane triangle the sides are proportional to the sines of the opposite angles. 1) D Let ABC be any triangle ; a, b, c the sides opposite the angles A, B, c respectively ; then will...
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A treatise on elementary trigonometry. [With] Key, by H. Carr

John Bascombe Lock - 1882
...bcosC + c cos 5. [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 4 sin B sin C ' From A, any one of the angular points, draw AD perpendicular...
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Introduction to Plane Trigonometry

Thomas Grenfell Vyvyan - 1882
...- = ^1 + sin^ - ,/1 - sin A. Is the formula true when A =240° ; if not how must it be modified? 7. In any triangle the sides are proportional to the sines of the angles opposite to them. 8. Having given two angles of a triangle and one of the sides, shew how to...
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Cambridge University Examination Papers

University of Cambridge - 1884
...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 - B /(s -a)...
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A Treatise on Higher Trigonometry

John Bascombe Lock - 1884 - 208 sider
...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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A Treatise on Elementary Trigonometry

John Bascombe Lock - 1885 - 274 sider
...=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 AD perpendicular...
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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, having given...
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