Calendar: 1851-1852 Page 365

THE SCHOOL 309 Find χ from the following equations tan tan sin ע cos χ 7T cot cot χ j- JL 12 Prove the identities sin Λ sin sin sin ל י sin -f sin Λ --j- -- tan cos cos tan 30 tan 30 c0S 2g j- cos If in triangle sin sin β -f sin then β In the equation χ f0 the two values of are ע cos and ρ sin 2- if sin צ ρ1 In order to ascertain the height of mountain hase of 2761 feet was measured and at either extremity of the base the angles formed by the summit and the other extremity were taken these were 58 29 and 111 52 also at the extremity where the latter angle was taken the angular height of the mountain was 11 18 Find its height Log sin 58 29 93069 log 2761 44107 Log sin 170 21 22435 log 2751 43955 Log sin 11 18 29214 Given the radius of circle find the area of the inscribed dodecagon Sum the series tan tan a- tan -A4- &c to infinity