Calendar: 1880-1881 Page 641

GENERAL LITERATURE AND SCIENCE 641 If θ be the circular measure of small angle shew thai cos θ and -I-- 16 Shew how the sines of angles which form an Arithmetical Progression having 10" for the common difference may be practically calculated Shew how to solve triangle when two sides and the included angle are given Shew also how the third side may be determined at once by the use of subsidiary angle Find the radii of the inscribed and escribed circles of triangle in terms of its sides If rx be the radius of the circle escribed on the side &c shew that r2 Assuming that the lines AD BE CF bisecting the angles meet where and are the points where AG BG9 and CG meet the opposite sides and are the sides of the triangles Shew that 10g 0geCt י and that 11 θ sin sin20 sin 30 ac Express the cosine of an angle in triangle and the cosine of double of the angle in terms of the sides of the triangle D' are the vertices of equilateral triangles constructed on the same base BC any other point if be the lengths of the sides of the triangle ABC shew that AD2 AH2 έ2