# Calendar: 1883-1884 Page 622

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i 618 GENERAL LITERATURE AND SCIENCE Prove that 16 cos 12 cos 24 cos 48 cos 96 Prove without assuming Euclid II 12 that c2 a2 -h £2 ab cos Why is this not convenient formula for the solution of triangles How is the inconvenience remedied Simplify sin-1 sin θ cos Θ -f sin-1Vsin 2Θ יx 2x -1 ζ2 tan-1 --- tan-1-7 tan-1 Λ V3 ν3 Find the distance of the circumcentre of triangle from the orthocentre and of the mid-centre from an angular point Shew that there are two cases in the solution of spherical triangles that may lead to an ambiguity Examine in particular the circumstances under which the solution is ambiguous when we have given both and being greater than right angle Prove that there can be only regular polyhedra and find the inclination of two adjacent faces of an icosahedron If rope be made of wires of diameter inches the number of wires in square inch of section is very nearly 10 plane parallel to the'base of cone divides the volume in the ratio and the curved surface in the ratio find the relation between η and 11 What measurements should you take to find the area of triangle of quadrilateral 12 Obtain rules for finding the following volumes pyramid on any base the portion of right prism in- eluded between two planes 13 mass of lbs has been falling under gravity for seconds give referred to consistent set of units the numerical measures of the distance it has fallen its velocity its momentum its kinetic energy the force that is changing its motion the rate at which it is receiving kinetic energy its acceleration

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