Calendar: 1859-1860 Page 449

450 GENERAL LITERATURE AND SCIENCE Given the side of the base of square pyramid and 2a the length of the edge find the inclination of the face to the base In triangle sin sin Β sin and sin B-C sin C-A sin A-B Prove that c2 a2 b2 cos and if tan θ that tan 1- A-3 tan tan 20 -- Β is an equilateral triangle inscribed in circle take any point Ρ in arc BC join AP Β CP then iP iP CP Find the distance of place from three known places all being in one plane having observed the angles SB SC Ex LetASB 30 ASC 75 AB ΒC AC Find all the values of θ when sin θ sin sin θ sin θ 16 sin b6 If cos sin cos sin sin cos cos cos ί 10 The interior angles of decagon are in arithmetical pro- gression the least angle being of the greatest angle Find the least and greatest angle 11 Find the distance between the centres of the circle inscribed in and of the circle described about given triangle 12 If sin η sin show that η must be less than and not less than Find when η θ β θ 13 Prove that sin θ 2" cos cos cos sin 2" 14 Show that when Θ cos θ and fl 51