...triangle, to the angles of the triangle; determine the radius of the circle. 59. Having given the ratio of the sines of the angles of a plane triangle, and the radius of the inscribed circle ; determine the sides and angles. 60. In an oblique-angled triangle ACB, having given the difference...

..., sin 6 = 2 and thence prove that sin AA — . = cot — . I -cos A" ""' 2 10. Given the ratios of the sines of the angles of a plane triangle, and the...of the inscribed circle, to construct the triangle. 11. Find the values of 6 which satisfy the equation 1823 2 sin2 30 + sin2 66 — 2, radius being =...

...through the angle of a given equilateral triangle. 56'. Having given the hypothenuse of a right-angled triangle, and the radius of the inscribed circle, to construct the triangle. 57. Having given the vertical angle of a triangle, and the radii of the inscribed and circumscribed...

...inversion. When the mercury in this barometer stands at 28 inches, what is the true altitude 1 37. The orifices in the equal bases of two upright prismatic vessels are m the ratio of 2 to 1, and the vessels are emptied in equal times ; what is toe ratio of their altitudes...

...volume which would have been discharged in the same time had the vessel been kept constantly full. 204. The orifices in the equal bases of two upright prismatic vessels are in the ratio of 2 : 1, and the vessels are emptied in equal times ; compare their altitudes. 205. Divide a cylinder 14...

...inversion. When the mercury in this barometer stands at 28 inches, what is the true altitude ? 37. The orifices in the equal bases of two upright prismatic vessels are in the ratio of 2 to 1, and the vessels are emptied in equal times ; what is the ratio of their altitudes ? 40 469 OF...

...volume which would have been discharged in the same time had the vessel been kept constantly full. 15. The orifices in the equal bases of two upright prismatic...emptied in equal times ; compare their altitudes. 16. Divide a cylinder 14 feet long, filled with fluid, into two such parts, that the times of emptying...

...also the radius of the inscribed circle, required to construct it. 36. Given the three angles of a triangle, and the radius of the inscribed circle, to construct the triangle. 37. If the base and vertical angle of a plane triangle be given, prove that the locus of the centers...

...volume which would have been discharged in the same time had the vessel been kept constantly full. 15. The orifices in the equal bases of two upright prismatic...emptied in equal times ; compare their altitudes. 16. Divide a cylinder 14 feet long, filled with fluid, into two such parts, that the times of emptying...

...is equal to the diameter of the inscribed circle. 32. Having given the hypotenuse of a right-angled triangle, and the radius of the inscribed circle, to construct the triangle. 33. ABC is a triangle inscribed in a circle, the line joining the middle points of the arcs AB, AC,...