. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. As radius 90° : tang. Z BAG 33° :: 120 feet 10COOOOOO9-81251742*0/91812 : 77*9289 feet= BC 18916986 The distance from the bottom of the tower to the near-er tree. Then, As radius 90° : tang. BAD 64° 30 :: BA 120 lOOOOOOOO 10*3215039 2C 91812 : BD 251*5852The distance of the farther tree. 2-4006651 Therefore BD — BC =251*5852 — 77*9289= 173*656feet = CD the distance between the two II. N 98 MATHEMATICS. PROBLEM
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. As radius 90° : tang. Z BAG 33° :: 120 feet 10COOOOOO9-81251742*0/91812 : 77*9289 feet= BC 18916986 The distance from the bottom of the tower to the near-er tree. Then, As radius 90° : tang. BAD 64° 30 :: BA 120 lOOOOOOOO 10*3215039 2C 91812 : BD 251*5852The distance of the farther tree. 2-4006651 Therefore BD — BC =251*5852 — 77*9289= 173*656feet = CD the distance between the two II. N 98 MATHEMATICS. PROBLEM IV. To find the perpendicular height of an object on a level, whenthe uaae, or tower end of the perpendicular^ is inaccessible. EXAMPLES. 1. What is the perpendicular height of a hill, whoseangie ol tlevation, taken at the bottom of it, was 46° ; and100 yards iarther off, on a level with the bottom of it, theangle was 31° ?. ZCZD 4631 } Subtract ZDDC BC 3C 15 94129962 31 9*7118393 100 20000000 2*2988431 AA 90° lOOOOOOOO ZC 46 9*8569341 CB 2*2988431 AB 143-14 2-1557772 HEIGHTS AND DISTANCES. 99 2. Wanting to know the height of an inaccessible object;at the least distance from it, upon the same horizontalplane, I took its angle of elevation equal to 58°, and going100 yards directly farther from it, found the angle thereto be only 32°: required its height, and my distance fromit at the first station, the instrument being 5 feet above theground at each observation.
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