Calendar: 1876-1877 Page 585

GENERAL LITERATURE AND SCIENCE 585 21 Explain clearly and illustrate by figures the ambiguous case in the solution of triangle 22 Two sides of triangle are and feet and the included angle is 120 find the other angles having given og-18 6812412 Ztan8 129 1586706 diff for 1000894 23 On the bank of river stands column 200 feet high supporting statue 30 feet high the statue to an observer on the opposite bank subtends an angle equal to that subtended by man feet high standing at the base of the column Shew that if the height of the observer's eye from the ground be neglected the width of the river is 10 V115 feet 24 If rr denote the radii of the inscribed and escribed circles of triangle the area and the semi-perimeter of the triangle prove rs Ss r2 r3 4Λ 25 Find the area of regular polygon of η sides described about circle of radius Deduce the expression for the area of the circle Three equal circles of radius touch each other shew that the area ot the space between them is v3- 26 Shew that tan-11 tan-11 tan-1-1 tan ο δ tan ϊ cos-' -4- tan "י -- cos- XVII -uPIane anlj £pljerical Crigonometr Prove that sin3 sin -f- sin 33 sin in3y sin β in2ly jS sin2 -- sin2 3- aj β