. 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°: tangent of 70°: : AB 80 feet ,c 219*798 feet lOOOOOOOO 10*4389341 19030900 2*3420241 HEIGHTS AND DISTANCES. 97 2. From the top of a tower, whose height was 120feet, I took the angle of depression 6i* two trees, which layin a direct line upon the same horizontal plane, with thebottom of the tower, viz. that of the nearer 57°, and thatof the farther 25°-| ; A\hat is the distance of each fromthe bottom of the
. 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°: tangent of 70°: : AB 80 feet ,c 219*798 feet lOOOOOOOO 10*4389341 19030900 2*3420241 HEIGHTS AND DISTANCES. 97 2. From the top of a tower, whose height was 120feet, I took the angle of depression 6i* two trees, which layin a direct line upon the same horizontal plane, with thebottom of the tower, viz. that of the nearer 57°, and thatof the farther 25°-| ; A\hat is the distance of each fromthe bottom of the tower, and their distance from eachother ?. 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° ?
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