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 176
angles of a rig4tt-angled triangle being 48 and 60 respectively, to determine the threesides of the triangle. MENSURA riON. 161 Solution. (1) Let BC=*. AC=nx, AB= mx, AD=48=a, BE=60= b. (2) AB2=AC2 + BC2, or m*x* —n2x2-\-x1, or w2=tt2+l. (3) .-. m2—n2=l ... (1). (4) Area ABC = area BAD + area DAC.… … (10) From triangle, DAC = cos|A = AD (11) .*. am-\-an 2mh1x ■ (2) (12) Similarly from area ABC = area ABE+area CBE. (13) We find *+«*==^p . . . (3). (14) <8)-H3) gives g+^W... (4). (15) Eliminating n, using (1) and (4), and calling -j^— d =.64. (16) w6+2/«5—{l+2d)m*— (4+2</)w3 — (\-2d)m1 +…
Arithmetic · Geometry
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