Calendar: 1870-1871 Page 520

520 GENERAL LITERATURE AND SCIENCE 18 If Α' B' are the external angles of triangle show that be vers ca vers Bt- -2ab vers ί 19 In any triangle prove that sin sin Β sin 20 tan cot £ Λ 21 The elevation of tower 100 feet high when due of an observer was 60 what will it be after he has walked due 400 feet given tan 13 53217166 tan 13" 54247475 22 In the triangle ABC given 22 30 20 find Β and it being given that log cot 11 10 711347 log tan 45 4810 0121294 log tan 45 490 0123821 log 3010300 23 ABC is triangle from AD is drawn at right angles to BC and from BE is drawn at right angles to AC show that DE cos 24 The number of sides of one polygon is four times that of another and the angles of the first one-half as large again as those of the second How many sides has each 25 Find the length of an arc subtending an angle of 60 in circle whose radius is 105 feet 26 If be the angle whose arc is rv and radius r2 and a1 be the angle whose arc is rs and radius ru then T-4 27 What distance is travelled in half an hour in consequence of the earth's rotation by person situated in latitude 60 taking the radius of the earth to be 000 miles 28 In any triangle show that vi ι η 2λ sin sin cos cos Β cos -- 29 Show that tan θ tan 60 tan 60 tan 30 Show that χ cos φ -1 χ sin φ tan ----tan-- φ χ 111 φ cos φ