A complete and practical solution book for the common school teacher . 164 FAIRCHIL&S SOLUTION BOOK. :. 5V3 = HC=FD+DG+ED. PROBLEM 347. Three horses are tethered each to a rope 15 rd. in length to the cor-ners of an eqilateral triangle whose side is 30 rd: over how much spacecan they graze, and how much remains ungrazed? Solution. (1) Let ABC be the triangle. CFD, BDE and AFE=the threesectors grazed over by thehorses. 0=space ungrazed. (2) Since the angle of an equilateral triangle is 60°, because thethree angles of every triangleare equal to two right angles,each sector is \ of a t
A complete and practical solution book for the common school teacher . 164 FAIRCHIL&S SOLUTION BOOK. :. 5V3 = HC=FD+DG+ED. PROBLEM 347. Three horses are tethered each to a rope 15 rd. in length to the cor-ners of an eqilateral triangle whose side is 30 rd: over how much spacecan they graze, and how much remains ungrazed? Solution. (1) Let ABC be the triangle. CFD, BDE and AFE=the threesectors grazed over by thehorses. 0=space ungrazed. (2) Since the angle of an equilateral triangle is 60°, because thethree angles of every triangleare equal to two right angles,each sector is \ of a three sectors=^ of acircle. (3) Area of circle, radius 15 rd. = 152X7r = 2257r sq. (4) 225k-^2^ sq. rd.^area grazed over. (5) Area of CBA=BDaV3, or 152V3= sq. rd. (6) sq. rd— sq. sq. rd., part not grazed FIG. 38. rd. PROBLEM 348. A goat is tethered by a cord 30 ft. long, to the corner of a shed intthe form of an equilateral triangle, side 20 ft.: find area over which itmay graze outdide of the shed. Solution. (1) Let ABC be the shed. (2) The goat can graze with the 30 ft. cord over a cir-cle, except a sector of60°, or angle A. (3) EMD=300°, or JU=f oi a circle, which has 302?rX|= sq. ft. (4) Angle DCS=120°, and angle EBS = 120°. (5) Angle EBS+angle DCS= 240°, or | of circle with aradius of 10 ft. (6) .. The area of BES+SCD=10*irX|-= sq. ft.
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