 | Mathematics - 1835 - 684 pages
...sides, angles, Sfc. of Triangles, or regular Poly* goni inscribed in, or circumscribed about it. (53.) THE sides of a triangle are proportional to the sines of the opposite angles. Let А, В, С be the angles, a, 6, с the sides opposite to them respectively of the triangle ABC.... | |
 | Harvey Goodwin - Mathematics - 1846 - 500 pages
...we must investigate certain formulae connecting the parts of a triangle. 104 PLANE TRIGONOMETRY. 29. The sides of a triangle are proportional to the sines of the opposite angles. FIG. 1. FIG. 2. CD Let ABC be a triangle. From any angular point A let fall the perpendicular AD on... | |
 | Education - 1851 - 502 pages
...formulae for the values of the opposite side (a), and the remaining angles (B, C). SECTION IV.—1. Prove that the sides of a triangle are proportional to the sines of the opposite angles. 2. Find the value of sin. 18°. 3. The elevation of a tower is observed from a certain distance. At... | |
 | George Wirgman Hemming - 1851 - 176 pages
...TRIANGLES. PAGE 51. When three parts of a triangle are given, it can generally be solved 83 52 — 53. The sides of a triangle are proportional to the sines of the opposite angles 84 54. To express the cosine of an angle of a triangle in terms of the sides 85 56. On the solution... | |
 | Bartholomew Price - 1856 - 672 pages
...forces p, Q, R are proportional to the three lines OP, OQ, OR, or to OP, PR', R'OJ and since the three sides of a triangle are proportional to the sines of the opposite angles, therefore -J— = . Q = . R „ (29) sin OR' P sin a OP SIDOPE p QR or = = , sin a sin j3 sm y that... | |
 | Royal University of Ireland - Universities and colleges - 1859 - 490 pages
...three and less than four. Write the value of this ratio as far as five places of decimals. 17. Prove that the sides of a triangle are proportional to the sines of the opposite angles. 18. Given two sides and the included angle of a triangle, find the remaining side and angles. 19. Prove... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1859 - 140 pages
...as the arc varies through a circumference. 10. Prove that in a plane triangle«a=6-+c2-26ccosA. 11. The sides of a triangle are proportional to the sines of the opposite angles. Prove this. 12. Investigate formula) for the solution of the different cases of plane triangles. 13.... | |
 | Denison Olmsted - Physics - 1860 - 492 pages
...component, it is not in the line of its action, because both forces act through the same point A. 46. Since the sides of a triangle are proportional to the sines of the opposite angles, these sines may also represent two components and their resultant. Thus, the sine of CAD corresponds... | |
 | Thomas Kimber - Mathematics - 1865 - 302 pages
...sin. (A — B), cos. (A + B), cos. (A — В). What is the numerical value of sin. 30° ? 7. Prove that the sides of a triangle are proportional to the sines of the opposite angles. (Oct. 27iA. — Rev. Prof. HEAVISIDE.) 8. Find by means of rectangular co-ordinates, the length of... | |
 | Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...generally denoted by А, В, C, and the sides respectively opposite to them by а, b, с. PROPOSITION I. The sides of a triangle are proportional to the sines of the opposite angles. Let А В С be any triangle, and from A let fall the perpendicular AD on В С, or В С produced,... | |
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The sides of a triangle are proportional to the sines of the opposite angles. 
