 | Woolwich roy. military acad - 1861 - عدد الصفحات: 572
...base. 7. Calculate by logarithms, /42-666N" /-0765Y V T147 / X\l-9432/ 8. In any plane triangle show that the sines of the angles are proportional to the opposite sides. Show that sin (C-30°)=c2 + 2Jc sin (A-30°). 9. The elevations of two mountains in the same line with... | |
 | 1869 - عدد الصفحات: 104
...will average 0° 15' 37.46', the proportion being as 3.6697 to 1 (Sec. 177) : Hence by the theorem that " the sines of the angles are proportional to the opposite sides," we have 195. In the triangle ABC, we have known the side AB by the last proportion, and the angle at... | |
 | Sidney Luxton Loney - 1905 - عدد الصفحات: 332
...that C3 = aa + 6!1-2a6cos C, and o* = 6a + ca— 2bc cos A. i,. MH 19 14. In any triangle to prove that the sines of the angles are proportional to the opposite sides, ie that sin A sin B _ sin C a ~ b *»= ,£_ "\ AD In Fig 1. we have — j— = sin C. In Fig. 2, we... | |
 | Cambridge Philosophical Society - 1838 - عدد الصفحات: 612
..._ b sin (a - A) y ~ a ' sin (ft — B) ' x _ c sin (a - A) * "a'sm(y- C) ; y _ c sin (ft — B) * ~ b ' sin (7 - C) ' These formulae, which are remarkable...lines D'A, D'B', DC meet in a point D', the angles A'D'li', BDC, ADC being equal to ADB, 13 DC, ADC respectively. At A any point in D'A make the angles... | |
 | Sidney Luxton Loney - 1953 - عدد الصفحات: 346
...relation. Similarly, we could prove that and o2 = 62 + c2 — 2bc cos A. 14. In any triangle to prove that the sines of the angles are proportional to the opposite sides, ie that In Fig. 1, Art. 13, we have - =aiuB. c AD In Fig. 2, we have - = sin A BD = sin (180' - B)... | |
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Their evident analogy to the property of a triangle " that the sines of the angles are proportional to the opposite sides", has suggested another form under which they may be put. 