A complete and practical solution book for the common school teacher (1899)
Fairchild, J[ohn] T[heodore] [from old catalog] · Crawfis College, Ohio, The author · leaf 252
what distance will a duck swim in unwindingthe string, keeping it taut at all times, the cone standing on its baseand at right angles to the surface of the water? Solution. (1) Let/; = height, r=radius of base, /=V (//2+r2)= slantheight, n = num-ber of spirals. (2) Let D, E be thetwo… … FIG. 122. 238 FAIRCHIL&S SOLUTION BOOK. (7) ^2 = DN2+NE2 . . . (1). (8) From the similar triangles GOF and DFE, r : GF=FD : DN. (9) .-. DN=(FD.GF)-^ . . . (2). (10) From the triangles LMK and KFD, dx : MK=^ : DF. (11) FD=^.MK^^ . . . (3). (12) MK : (/—*) = GF :/. (13) MK=[(/-j).GF]^/ ... (4).…
Arithmetic · Geometry
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