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" Ans. ^. 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a, b, c) of a triangle, and if A be the angle opposite to the side a, prove that o sin A = T-... "
Elements of Trigonometry, Plane and Spherical - Page 49
by Edward Olney - 1872 - 201 pages
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...parallel planes be cut by another plane their common sections with it are parallel. 6. Prove that the sides of any plane triangle are proportional to the sines of the opposite angles. Assuming the expression for the cosine of an angle in terms of the sides, find the...
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Elements of Trigonometry: Plane and Spherical

Edward Olney - Trigonometry - 1885 - 222 pages
...Prop — The sldes of any plane trlangle are proportional to the sines of the angles oppositeDEM — Let ABC be any plane triangle- Let fall from either...produced- Designate the angles by A, B, and C, the sidea opposite by a, 6,and c, and the perpendicular by PNow, from the right angled triangle ADC we...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...SIDES AND TRIGONOMETRICAL FUNCTIONS OF THE ANGLES OF OBLIQUE ANGLED PLANE TRIANGLES. 85. Prop* — The sides of any plane triangle are proportional to the...opposite. DEM. — Let ABC be any plane triangle. Let fell from either angle, as C, a perpendicular upon the opposite side, or upon that side produced. Designate...
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Plane and Spherical Trigonometry

George Albert Wentworth - Trigonometry - 1882 - 160 pages
...that sin A sm B sin С 6. Given that sin^.4 = f , find the value of tan .4. Ans. fy. 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a, b, c) of a triangle, and if A be the angle opposite...
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Military examinations. Mathematical examination papers set at an open ...

Civil service commission - 1883 - 62 pages
...and sec 2 e = - s- = 3. cos 2 e Therefore sec-1 3 = 2 e = 2 cot-1 л/2. QED 12. — Prove that the sides of any plane triangle are proportional to the sines of the opposite angles. Prove also that in any plane triangle . В - С _ , A a sin — - — = (6 — c)...
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Plane and Spherical Trigonometry: G. A. Wentworth ...

George Albert Wentworth - Trigonometry - 1884 - 330 pages
...sin A sin B sin C 6. Given that sin ^.4 = •£, find the value of tan.4. Ans. "£. 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a, b, c) of a triangle, and if A be the angle opposite...
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Plane Trigonometry

George Albert Wentworth - 1887 - 206 pages
...that sin A sin B sin C 6. Given that sinA A = f , find the value of tan A. Ans. ^. 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a, b, c) of a triangle, and if A be the angle opposite...
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Five-place Logarithmic and Trigonometric Tables

George Albert Wentworth - 1887 - 346 pages
...sin A sin B sin G 6. Given that sin 4.4 = f , find the' value of tan A. Ana. V-- 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a, b, c) of a triangle, and if A be the angle opposite...
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...A. (2) tan (60° + A)- tan (60° - A) = 8 C0t A cotM — 3 (3) sec-i 3 = 2cot~V2. 12. Prove that the sides of any plane triangle are proportional to the sines of the opposite angles. Prove also that in any plane triangle . B - C ,, . A a sin = (b - c) cos — . 2 2...
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Coal Miners' Pocketbook: Formerly The Coal and Metal Miners' Pocketbook ...

Thomas J. Foster - Coal mines and mining - 1916 - 1230 pages
...apply to all triangles, but are of particular service in solving those with oblique angles: 1. The sides of any plane triangle are proportional to the sines of the angles opposite. a : b = sin A : sin B a : c — sin A : sin C b : c=sin B : sin C 2. Any side of a plane triangle equals...
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