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 96by George Albert Wentworth - 1887Full view - About this book
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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)... | |
| 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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