; TeX output 1996.02.23:0911*(+؍V"V cmbx1018.019PR9OBLEM9SET1{SOLUTIONS$ 12.KV!iK`y cmr10(158+=V !", cmsy10p 7=Vfeª220:)ٓRcmr75C=e155S+85154=Vp 7=Vfeª220+10153(=VpUW=Vfeª220UZ)2+10152(=VpUW=Vfeª220UZ)3|s+h+8515(=VpUW=Vfeª220UZ)4S+(=VpUW=Vfeª220)5!i(158=Vp 7=Vfeª220:)5C=e155S85154=Vp 7=Vfeª220+10153(=VpUW=Vfeª220UZ)210152(=VpUW=Vfeª220UZ)3|s+h+8515(=VpUW=Vfeª220UZ)4S(=VpUW=Vfeª220)5|s b> cmmi10; 9henceq[(158+=Vp 7=Vfeª220:)5S+(15=Vp 7=Vfeª220)5C=2155S+210153(220)+2515(220)2Ѝ9isv)indeedaninteger,~^divisibleby10.D(15N÷Pp PfeE220)^5zB<ϫ1,~^sov)thelastdigitpreceding z9theUUdecimalpGointinthedecimalexpressionof(158+Pp 7PfeE220:)^5ȫisUU9. Kd(3UUpGoints)L 13.&9UsingUUsimilartrianglesj<$^t]͸wfeI0 (֍ag3=<$sinzJKwfe (֍cos7=tan㊱G:Ѝ9ButUUa=1,sot=tan㊱G.qSimilarly*,<$M>sLگwfe (֍zU=<$ gtKwfeꪟ (֍sin Ʊ@=<$KtanKwfeV (֍Vsin =secGG:9AgainUUb=1,sos=secGG: &9The~similarstatementsforcot}andcscP{are9shownMonthepicturetotheright.TheproGofof9thesestatementsarebasicallythesameasthe9onesUUfortanqDZrandsecRG.jtKd(3UUpGoints) 14.9TheUUareaoftheOGABƫtriangleis<$1wfe (֍2 fdsinX*.9TheUUareaoftheOGABƫcirclesectoris<$1wfe (֍2 .9TheUUareaoftheOGATtriangleis<$1wfe (֍2 fdtanֱ.h9ThebstatementnowfollowsfromthefactthattheOGAB triangleiscontainedin9theUUOGABƫcirclesector,whichiscontainedintheOGATtriangle.Kd(3UUpGoints)#N|{Ycmr8TÎyp cmmi10ٓRcmr7|{Ycmr8K`y cmr10