Question

如图,在三角形ABC中AB=AC,角BAC=90度,P点在BC边上BP=1,D点在AC边上若角APD=45度AC=3,C

Answer 1

∵⊿ABC中,AB=AC,∠BAC=90°,P在BC边上,BP=1,D在AC边上,∠APD=45° AC=3 ∴AP=√﹙3²+1²－2×3×1×cos45°﹚=2.399∴sin∠BAP=BP×sin45°／AP=0.2947∴∠BAP=17.14°∴AD=AP×sin45°／sin∠ADP=AP×sin45°／sin﹙180﹣45﹣＜90﹣17.14＞﹚°=1.919∴CD=3﹣1.919=1.081