| War office - 1861 - 12 sider
...tan 2 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... | |
| Benjamin Greenleaf - 1862 - 490 sider
...product of the other side into the cotangent of the angle. TRIGONOMETRY. (87) (88) 111. In any plane **triangle, the sides are proportional to the sines of the opposite angles. Let ABC be any triangle,** in which the sides opposite the angles A, B, C, respectively, are denoted by a, b, and c. From one... | |
| Benjamin Greenleaf - 1861 - 490 sider
...= — , ^ P b=p tan 7?. (87) therefore b = p cot «**=£, p = i cot 5. (88) 1 1 1 . /.< any /(fane **triangle, the sides are proportional to the sines of the opposite angles.** B Let ABG be any triangle, in which the sides opposite the angles A, B, C, respectively, are denoted... | |
| Benjamin Greenleaf - 1862 - 490 sider
...RELATIONS BETWEEN THE SIDES AND ANGLES OF SPHERICAL TRIANGLES. 148. In any spherical triangle, the sines of **the sides are proportional to the sines of the opposite angles. Let** А В С be any spherical triangle ; А, Д and С the angles opposite to its sides a, b, and c, respectively;... | |
| Benjamin Greenleaf - 1863 - 320 sider
..., therefore b = p cot .4, -*=£, b = p tan B. cot B = ~- , p = b cot 5. (87) (88) 111. In any plane **triangle, the sides are proportional to the sines of the opposite angles. Let ABC be any triangle,** in which the sides opposite the angles A, B, C, respectively, are denoted by a, b, and c. From one... | |
| Isaac Todhunter - 1864 - 279 sider
...each side is equal to the product of the cotangent of the adjacent angle into the other side. 214. **In any triangle the sides are proportional to the sines of the opposite angles.** D Let ABC be any triangle, and from A draw AD perpendicular to the opposite side meeting that side,... | |
| Thomas Kimber - 1865 - 192 sider
...Show that cos. (A — В) = cos. A cos. В + sin. A sin. B. Find the cosine of 15°. 12. Show that **in any triangle the sides are proportional to the sines of the opposite angles.** Hence, deduce the expression for the cosine of an angle of a triangle in terms of the sides. 13. Find... | |
| John Walmsley - 1865 - 182 sider
...a, b, с for the sides respectively opposite to them. 88. In any triangle the sides are respectively **proportional to the sines of the opposite angles. Let ABC be any triangle.** Draw CD perpendicular to AB, falling (1) within the triangle, and (2) without it. In (2) the angles... | |
| Isaac Todhunter - 1866 - 192 sider
...oblique-angled triangles as well as for acute- angled triangles. We retain the notation of Art. 37. 104. **In any triangle the sides are proportional to the sines of the opposite angles. Let** ABO be a triangle, and from A draw AD perpendicular to the opposite side, meeting that side, or that... | |
| James McDowell - 1866
...definition, ta.nA = cotB = T. o tanB = cotA = -; .-. a = b tanA = b cot-B, b = a tan.B= a cot A. 52. **In any triangle the sides are proportional to the sines of the opposite angles.** (4) (2) a Let ABC be any triangle, and from A draw AD perpendicular to BC or BC produced. From the... | |
| |