Calendar: 1893-1894 Page 840

cxv111 FACULTY OF SCIENCE If CHK is an equilateral triangle inscribed in square ABCD so that Η is on AB and Κ on AD prove that Am twice AB BH If the sides of triangle are given establish method of finding its angles and area The sides of triangle are 345934 4876 57 and 4159-62 yards find its area to the nearest square yam ana 11s greatest angle to the nearest minute Use tables man at the base of straight road up hill notices that it is inclined at constant angle to the horizon and if he retires distance feet along straight horizontal road in the same vertical plane as the hill that the angle of elevation of the centre of the inclined road is β Find the length of the inclined road If an error is made in measuring the angle β prove that the consequent error in the 'calculated length is approxi mately 2ax sin sin2 β person at the top of tower 100 ft high observes that the angle of depression of point due east of him on the top of wall running north and south is 45 while that of an object at the foot of the wall in north-easterly direction is cot-1 '9 V2 Find the height of the wall Express the area of regular polygon of η sides in- scribed in circle of radius An inner polygon is formed by joining the middle points of adjacent sides of the former Shew that the area between the polygons is to the area of the outer as sin2 η Find the sum of the series 7r 27r 37r η 7r cos cos-- cos -f cos ג -9 -י η η η '' η when η is positive integer 10 Give an account of the method of forming table of sines