A complete and practical solution book for the common school teacher . (10) BC=V(BE» + UE») = 4^/673=+. (11) OG=£ofl5=5. FG=v/OG2-TyF2 (12) CF=«+V=W- (13) CO=T/[(W) + (»)a]=ii/592=+. FIG. 50. 8 8 PROBLEM 364. In a triangular garden whose sides are a=300 ft., 6=250 ft., and£=200 ft., is a spring equally distant from each corner: how far is itfrom each corner? Solution. (1) Let BAC be the garden. (2) CA=300 ft., BC=250 AB=200 ft., and O represents the position olthe spring. (3) BO, OA and OC are radii of the circumscribingcircle and the requireddistance. (4) Let g±|±£ =s; then,
A complete and practical solution book for the common school teacher . (10) BC=V(BE» + UE») = 4^/673=+. (11) OG=£ofl5=5. FG=v/OG2-TyF2 (12) CF=«+V=W- (13) CO=T/[(W) + (»)a]=ii/592=+. FIG. 50. 8 8 PROBLEM 364. In a triangular garden whose sides are a=300 ft., 6=250 ft., and£=200 ft., is a spring equally distant from each corner: how far is itfrom each corner? Solution. (1) Let BAC be the garden. (2) CA=300 ft., BC=250 AB=200 ft., and O represents the position olthe spring. (3) BO, OA and OC are radii of the circumscribingcircle and the requireddistance. (4) Let g±|±£ =s; then, by 2formula. CD= -Vs{s- a)\s—b) (s—c) —. 248+.(5) Now as the triangles CBD,CB :CE::CD: CA. FIG. 51. CAE ate similar, we have MENSURATION. 175 (6) Substituting the values of CB, CD, CA in the above pro-portion, we find CE, the diameter of the circle = 302-|- ft. .-. BO, AO and CO = 151+. NoTB.—This problem was taken from the Teachers1 Review. Thesolution there is different from the one above. PROBLEM 365. A mathematical teacher amuses six of his best students by laying-off a triang-ular space on the level school yard, measuring- exactly231 ft., 250 ft. and 289 ft. He takes his position in the center, threeboys occupy positions on the vertices and three girls on the sides equi-distant from the teacher. The girls figure the distance they are fromthe teacher, and the boys find out how far each is from the teacher andthe two nearest girls. {Hancock Co. test) Solution. (1) Let ABC be the tri- angle, and O the posi-tion of the teacher,A, B, C the positionsof the boys, and S, D,K that of the girls. (2) Let AB=c, CB=a and CA=£, an
Size: 1587px × 1574px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1890, booksubject, booksubjectgeometry
