Calendar: 1853-1854 Page 399

THE SCHOOL 395 FIRST CLASS MATHEMATICAL SCHOLARSHIP -Cvtcjonomttn airt fi lcci amc£ Λ Β is triangle line is drawn cutting in BO in and the base produced in show that- Ab Bc Ca Ac Ba Cb If tan -2 γ find sin and if- -1 7r cot -cot χ -f -- find χ 1Δ Given and the radii of the circumscribed and inscribed circles and the vertical angle of triangle find the other parts Assuming De Moivre's formula find by it the expansions of sin χ and cos tower 51 feet high has mark in it 25 feet from the ground at what distance from the foot of the tower do the two parts appear of the same magnitude to an eye feet above the ground triangular piece of wood is placed against and fills up the corner of room the angles being feet from the corner show that the area of wood sja2 b2 a2 cl 62 c2 Show that the resultant of two forces acting upon point is the diagonal of the parallelogram whose sides represent the forces CΒ are two beams jointed at and supported at find the position of equilibrium and the distance the centre of gravity ofthe beams is from body is supported on an inclined plane by the action of power inclined at given angle to the plane determine the equilibrium the plane being rough 10 Find the centre of gravity of the frustum of pyramid