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" 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 to the side a, prove that 2 _ 8. Prove that... "
Plane Trigonometry - Page 96
by George Albert Wentworth - 1887
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 pages
...right-angled plane triangle is (Art. 13. and E. 32. 1.) the cosine of the other. (21.) The sides of a plane triangle are proportional to the sines of the angles opposite to them. For, if a circle be described (E. 5. 4.) about any plane triangle, the sides (E. 21. 3. and Art....
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861
...bases. 5. If two 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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A Treatise on Special, Or Elementary Geometry

Edward Olney - Geometry - 1872 - 239 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 sines of the angles opposite. DEM. — Let ABC be any plane triangle. Let fell from either angle, as C, a perpendicular upon the...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872
...SIDES AND TIUGONOMETRIOAL FUNCTIONS OF THE ANGLES OF OBLIQUE ANOLKD PLAKE TRIANGLES. 85. Prop. — TJte sides of any plane triangle are proportional to the sines of the angles opposite. DEM.— Let ABC be any plane triangle. Let fall from either angle, as C, a perpendicular upon the opposite...
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Elements of Trigonometry, Plane and Spherical

Edward Olney - Trigonometry - 1872 - 201 pages
...8IDE8 AND TRIGONOMETRICAL FUNCTION8 OF THE ANGLES OF OBLIQUE ANGLED PLANE TRIANGLE8. 83. Prop. — Tl1e sides of any plane triangle are proportional to the sines of the angles opposite. DEM. — Let ABC be any plane triangle. Let fall from either angle, as C, a perpendicular upon the...
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A manual of telegraph construction

John Christie Douglas - Telegraph lines - 1875 - 468 pages
...The sum of the angles of a plane triangle is 180 — ie, equal to two right angles. The sides of a plane triangle are proportional to the sines of the angles opposite to them respectively. The square on the hypothenuse of a right-angled triangle is equal to the sum of...
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A Treatise on Special Or Elementary Geometry: Including an Elementary, and ...

Edward Olney - Geometry - 1879 - 440 pages
...SIDES AND TRIGONOMETRICAL FUNCTIONS OF THE ANGLES OF OBLIQUE ANGLED PLANE TRIANGLES. 85. Prop. — TJie sides of any plane triangle are proportional to the sines of the angles opposite. DEM. — Let ABC be any plane triangle. Let fall from either angle, as C, a perpendicular upon the...
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Plane and Spherical Trigonometry

George Albert Wentworth - Trigonometry - 1882 - 201 pages
...B. Hence show 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...A be the angle opposite to the side a, prove that 2 _ . sin A = ^ Vs (s - a) (s — b) (s — c). 8. Prove that in any plane triangle B) = — - cot...
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Military examinations. Mathematical examination papers set at an open ...

Civil service commission - 1883
...— sin* e = \, 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 - 6460 pages
....4 sin B. Hence show that 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...A be the angle opposite to the side a, prove that 2 sin A = 7- Vs (s — a) (s — b)(s — c). 8. Prove that in any plane triangle 9. If the side a...
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