Calendar: 1883-1884 Page 628

624 general literature and science 11 person observes the elevation of tower to be 30 and on advancing 100 yards nearer to it he finds the elevation to be 60 Required the height of the tower 12 Prove the following sin2 cos2 cos4 cos 2A sin4 sin2 3-48i1Arf l-3tan2 3-tan2 4cos2 -3 13 Give geometrical proofs for the expansions of sin and' tan and show that tan tan tan 2A 14 Show that in any triangle ABC sin sin Β &'ιΏ cos י cos cos י sin sin Β sin -r- -- 15 If 70 3512 52 36 ל ג" find the other angles having given log 4771213 cot 18 264771213 10 "6 16 Prove that the area of triangle is 2abc ABC cCOS2'cos2'cos2' 17 On the bank of river there is column 200 feet high supporting statue 30 feet high The statue to an observer on the opposite bank subtends the same angle as man feet high standing at the foot of the column Find the breadth of the river 18 The sides of triangle are in Arithmetical Progression and its area is to that of an equilateral triangle of the same perimeter as Find the ratio of the sides and show that its largest angle is 120 XV -Utomttw If two triangles have two sides of the one equal to two sides of the other each to each and have likewise the angles contained by those sides equal to one another they shall