Calendar: 1877-1878 Page 589

GENERAL LITERATURE AND SCIENCE 587 20 Solve triangle when two sides are given and the angle opposite to one of them Illustrate by figures the ambiguous case 21 If isin 9-5228787 10g3 4771213 find 22 An object is observed at points lying in bori zontal straight line which passes directly underneath the object tbe angular elevation at Β is twice that at and at is three times that at If AB BC shew that the height of the object is f6V 34 23 If rri r2 r3 denote the radii of the inscribed and escribed circles of triangle then ί r3 cotan2- cotan2- cotan2 Also the distances of the centre of the inscribed from the centres of the escribed circles are respectively Α Β sec sec sec 24 Prove tan-1- tan-11 tan-li tan-1 and shew that if tan ax sec-1 bx then one solution is tf2 2ai β2 XVII -aigtbra 31Λ torj of £q uattoni FIND the number of homogeneous products of dimensions which can be formed out of η letters and their powers Find the number of ways in which ρ things may be distributed to persons so that everybody may have one at least