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Llibres Llibres 1 - 10 de 120 sobre Law of Sines — In any triangle, the sides are proportional to the sines of the....
" Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... "
Plane Trigonometry - PÓgina 17
1906 - 188 pÓgines
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A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - 1808 - 480 pÓgines
...4-8░,4.8' 9-87G4-6 So is AC 126 2- 10031To BC 9*'S 1-97683 SECTION 1 1. Of oUiquc angular Trigonometry. In any triangle, the sides are proportional to. the sines of the opposite angles. When two angles of any triangle are given, their sum, being subtracted from 1 80░, leaves the third...
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A System of Plane and Spherical Trigonometry: To which is Added a Treatise ...

Richard Wilson - 1831 - 330 pÓgines
...а + cos — sin ▀ 2 ▀ _ tan a -▀ SECTION III. ON THE SOLUTION OF PLANE TRIANGLES. 108. PROP. In any triangle the sides are proportional to the sines of the opposite angles. For let ABC be the triangle. Let the angles be denoted by A, B, C,. and the sides opposite to them...
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Pantology: Or, A Systematic Survey of Human Knowledge; Proposing a ...

Roswell Park - 1841 - 587 pÓgines
...hypothenuse, as the cosine of the angle at the base, is to radius, or the sine of 90░. In an oblique angled triangle, the sides are proportional to the sines of the opposite angles : also, the sum of any two sides is to their difference, as the tangent of the half sum of the two...
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Elements of Plane and Spherical Trigonometry: With the First Principles of ...

James Bates Thomson - 1844 - 126 pÓgines
...ACD, BCD, CD=r AC sin A=BC sinB; whence (Euc. VI. 16) AC : BC : : sin B sin A ; that is, in any plane triangle, the sides are proportional to the sines of the opposite angles. Hence, also, ^nr; = - — — . ,,, . , TT i 22. One of the most important problems in trigonometry,...
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The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 451 pÓgines
...from the introduction of the demonstrations among the precepto for calculatiou. LVIII. In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be the triangle ; produce the shorter side, AB, to v F, making AF equal to BC ; from В and...
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Pantology

Roswell Park - 1847 - 580 pÓgines
...hypothenuse, as the cosine of the angle at the base, is to radius, or the sine of 90░. In an oblique angled triangle, the sides are proportional to the sines of the opposite angles : also, the sum of any two sides is to their difference, as the tangent of the half sum of ihe two...
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Elementary mechanics

Sir John Budd Phear - 1850 - 252 pÓgines
...triangle. The parallelogram and the triangle of forces are therefore identical propositions. 19. Since in any triangle the sides are proportional to the sines of the opposite angles, our proposition shews us, that of three forces keeping any point in equilibrium, each is proportional...
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Plane trigonometry. [With] Solutions of examples

John William Colenso (bp. of Natal.) - 1851
...ON THE TRIGONOMETRICAL PROPERTIES OF TRIANGLES, QUADRILATERALS, AND POLYGONS. 105. To shew that in any triangle the sides are proportional to the sines of the opposite angles. In future we shall use the letters a, J, c, to denote the sides BC, AC, AB, opposite to the angles...
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An elementary treatise on statics: with a biographical notice of the author

Gaspard Monge - 1851 - 216 pÓgines
...we may however enunciate this theory independently of all construction. Thus, in every triangle ABC, the sides are proportional to the sines of the opposite angles : that is to say, we have • AC : EC : AB : : sin ABC : sin BAC : sin ACB. Now, the sines of these angles are...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 pÓgines
...A v ' Sin 3 A — sin A (3) (Cos A + cos B)2 + (sin A + sin B)2 = 4 cos2i( A - B) 4. Prove that in any triangle the sides are proportional to the sines of the opposite angles. 6. The angular elevation of the top of a tower is observed to be 60░ 14'; the observer then retires...
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