¾«Ó¢¼Ò½ÌÍø£¨´´ÐÂÌ⣩£®ÎÒÃÇʹÓõÄÈý½Ç°åÖÐÓÐ30¡ã£¬45¡ã£¬60¡ãºÍ90¡ãÌØÊâ½Ç£¬ÎÒÃǹ涨£ºÓÉÒ»¸±Èý½Ç°åÖеĽǼӣ¬¼õËùµÃµÄ½Ç³Æ֮Ϊ¡±°ëÌØÊâ½Ç¡±£®Èç135¡ã=90¡ã+45¡ãµÈ£®ÈçͼÊÇÓÉÁ½¿éб±ßµÈ³¤µÄÈý½Ç°åÞÕ´Õ¶ø³ÉµÄ£¬
£¨1£©Ð´³öͼÖÐËùÓеÄСÓÚƽ½ÇµÄ¡±°ëÌØÊâ½Ç¡±ºÍËüÃǵĶÈÊý£»
£¨2£©ÀûÓÃͼÇósin15¡ãµÄÖµ£»
£¨3£©½«Í¼Öк¬30¡ã½ÇµÄÖ±½ÇÈý½Ç°åÑØAB·­Õ۵á÷ABC1£¬ÔÙ×÷¡÷ABC¹ØÓÚABÖеãOµÄÖÐÐĶԳơ÷ABC2£¬Á¬AC2£¬BC1£¬Ï߶ÎDC2£¬DC1·Ö±ð½»ABÓÚF£¬G£¬»­³öͼÐΣ¬Ö¸³öÆäÖеÄÁ½¶ÔÏàËÆÈý½ÇÐΣ¬²¢Çó³öÆäÖÐÒ»¶ÔÏàËÆÈý½ÇÐεÄÏàËƱȣ®
·ÖÎö£º£¨1£©¸ù¾ÝÌâÒâµÃµ½Èý½ÇÐÎABDΪµÈÑüÖ±½ÇÈý½ÇÐΣ¬Èý½ÇÐÎABCΪº¬30¡ãµÄÖ±½ÇÈý½ÇÐΣ¬¸ù¾ÝÌâÖеÄж¨Ò壬ÀûÓÃÌØÊâ½ÇµÄ¼Ó¼õ¼´¿ÉµÃµ½¡ÏDAC=¡ÏDBC=15¡ã£¬¡ÏAED=¡ÏBEC=75¡ã£¬¡ÏCED=¡ÏAEB=105¡ã£»
£¨2£©¹ýE×÷EFÓÚAB´¹Ö±£¬ÁîAD=BD=a£¬ÉèEF=x£¬ÔÚÖ±½ÇÈý½ÇÐÎABDÖУ¬¸ù¾Ý¹´¹É¶¨Àí±íʾ³öABµÄ³¤£¬Åж¨³öÈý½ÇÐÎBEFΪµÈÑüÖ±½ÇÈý½ÇÐΣ¬µÃµ½EF=BF=x£¬¸ù¾Ý30¶È½ÇµÄÕýÇÐÖµ£¬ÓÉEF=x£¬±íʾ³öAFµÄ³¤£¬ÓÉAF+FB=ABÁгöµÈʽ£¬Óú¬aµÄʽ×Ó±íʾ³öx£¬¸ù¾Ý30¶È½ÇËù¶ÔµÄÖ±½Ç±ßµÈÓÚб±ßµÄÒ»°ë£¬Çó³öAE=2x£¬±íʾ³öAE£¬ÓÃDB-BE±íʾ³öDE£¬ÔÚÖ±½ÇÈý½ÇÐÎADEÖУ¬ÓÉÕýÏÒº¯ÊýµÄ¶¨Ò壺¶Ô±ß±Èб±ß¼´DE±ÈAE¼´¿ÉÇó³ösin15¡ãµÄÖµ£»
£¨3£©¸ù¾ÝÌâÒâ»­³öͼÐΣ¬ÓÉÖ±½ÇÈý½ÇÐÎб±ßÉϵÄÖÐÏßµÈÓÚб±ßµÄÒ»°ëµÃµ½µãA£¬D£¬B£¬C1£¬C2¶¼ÔÚÒÔABΪֱ¾¶µÄÔ²ÉÏ£¬¸ù¾Ýͬ»¡Ëù¶ÔµÄÔ²ÖܽǶ¼ÏàµÈµÃµ½¡ÏADC2=¡ÏABC2=¡ÏBAC1=30¡ã£¬¡ÏDAB=¡ÏDBA=¡ÏCC1A=45¡ã£¬È»ºóÓÉÁ½¶Ô¶ÔÓ¦½ÇÏàµÈµÄÁ½Èý½ÇÐÎÏàËÆ£¬µÃµ½¡÷ADF¡×¡÷C1AG£¬¡÷ADC2¡×¡÷FDA£¬ÉèAD=BD=a£¬ÀûÓù´¹É¶¨Àí±íʾ³öAB£¬ÔÚRt¡÷ABC1ÖУ¬ÀûÓÃ30¶È½ÇµÄÓàÏÒº¯Êý¶¨Òå±íʾ³öAC1£¬ÓÃAD£ºAC1¼´¿ÉÇó³ö¡÷ADFÓë¡÷C1AGµÄÏàËƱȣ®
½â´ð£º½â£º£¨1£©¡ß¡ÏDAB=¡ÏDBA=45¡ã£¬¡ÏCAB=30¡ã£¬¡ÏCAB=60¡ã£¬¡ÏD=¡ÏC=90¡ã£¬
¡à¡ÏDAC=¡ÏDAB-¡ÏCAB=45¡ã-30¡ã=15¡ã£¬¡ÏDBC=¡ÏCAB-¡ÏDBA=60¡ã-45¡ã=15¡ã£¬
ÓÉ¡ÏAEDΪÈý½ÇÐÎABEµÄÍâ½Ç£¬
¡à¡ÏAED=¡ÏCEB=¡ÏCAB+¡ÏDBA=30¡ã+45¡ã=75¡ã£¬
ÓÉ¡ÏDECΪÈý½ÇÐÎADEµÄÍâ½Ç£¬¡ÏAEBΪÈý½ÇÐÎAEDµÄÍâ½Ç£¬
¡ÏDEC=¡ÏAEB=¡ÏDAC+¡ÏD=90¡ã+15¡ã=105¡ã£¬
×ÛÉÏ£¬¡ÏDAC=¡ÏDBC=15¡ã£¬¡ÏAED=¡ÏBEC=75¡ã£¬¡ÏCED=¡ÏAEB=105¡ã£»
¾«Ó¢¼Ò½ÌÍø
£¨2£©¹ýE×÷EF¡ÍABÓÚFµã£¬
ÁîAD=BD=a£¬EF=x£¬
ÔòAB=
2
a£¬BF=EF=x£¬AF=
3
x
¡à£¨
3
+1£©x=
2
a£¬
½âµÃ£ºx=
(
6
-
2
)a 
2
£¬
ÄÇôAE=2x=£¨
6
-
2
£©a£¬
DE=a-
2
x=£¨2-
3
£©a£¬
¡àsin15¡ã=
DE
AE
=
(2-
3
)a
(
6
-
2
) a
=
6
2
4
£®

£¨3£©ÓÉ¡±Ö±½ÇÈý½ÇÐÎб±ßÉÏÖÐÏßµÈÓÚб±ßµÄÒ»°ë¡±¿ÉÖª£¬
µãA£¬D£¬B£¬C1£¬C2¶¼ÔÚÒÔABΪֱ¾¶µÄÔ²ÉÏ£¬
Ôò¡ÏADC2=¡ÏABC2=¡ÏBAC1=30¡ã£¬¡ÏDAB=¡ÏDBA=¡ÏCC1A=45¡ã£¬
¡à¡÷ADF¡×¡÷C1AG£®¡÷ADC2¡×¡÷FDA£®
ÁîAD=BD=a£¬ÔòAB=
2
a£¬
ÔÚRt¡÷ABC1ÖУ¬AC1=ABcos30¡ã=
2
a•
3
2
=
6
a
2

ÓÉ¡÷ADF¡×¡÷C1AGµÃÏàËƱÈAD£ºC1A=2£º
6
£®
µãÆÀ£º´ËÌ⿼²éÁËÏàËÆÈý½ÇÐεÄÅж¨ÓëÐÔÖÊ£¬Ô²ÖܽǶ¨Àí£¬Ö±½ÇÈý½ÇÐεÄÐÔÖÊ£¬ÒÔ¼°Èñ½ÇÈý½Çº¯ÊýµÄ¶¨Ò壮ҪÇóѧÉú½èÖúͼÐΣ¬ÀûÓÃÊýÐνáºÏµÄÊýѧ˼Ï룬¹¹ÔìÖ±½ÇÈý½ÇÐΣ¬Áé»îÔËÓù´¹É¶¨Àí¼°Èñ½ÇÈý½Çº¯Êý¶¨ÒåÀ´½â¾öÊýѧÎÊÌ⣮
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

£¨´´ÐÂÌ⣩£®ÎÒÃÇʹÓõÄÈý½Ç°åÖÐÓÐ30¡ã£¬45¡ã£¬60¡ãºÍ90¡ãÌØÊâ½Ç£¬ÎÒÃǹ涨£ºÓÉÒ»¸±Èý½Ç°åÖеĽǼӣ¬¼õËùµÃµÄ½Ç³Æ֮Ϊ¡±°ëÌØÊâ½Ç¡±£®Èç135¡ã=90¡ã+45¡ãµÈ£®ÈçͼÊÇÓÉÁ½¿éб±ßµÈ³¤µÄÈý½Ç°åÞÕ´Õ¶ø³ÉµÄ£¬
£¨1£©Ð´³öͼÖÐËùÓеÄСÓÚƽ½ÇµÄ¡±°ëÌØÊâ½Ç¡±ºÍËüÃǵĶÈÊý£»
£¨2£©ÀûÓÃͼÇósin15¡ãµÄÖµ£»
£¨3£©½«Í¼Öк¬30¡ã½ÇµÄÖ±½ÇÈý½Ç°åÑØAB·­Õ۵á÷ABC1£¬ÔÙ×÷¡÷ABC¹ØÓÚABÖеãOµÄÖÐÐĶԳơ÷ABC2£¬Á¬AC2£¬BC1£¬Ï߶ÎDC2£¬DC1·Ö±ð½»ABÓÚF£¬G£¬»­³öͼÐΣ¬Ö¸³öÆäÖеÄÁ½¶ÔÏàËÆÈý½ÇÐΣ¬²¢Çó³öÆäÖÐÒ»¶ÔÏàËÆÈý½ÇÐεÄÏàËƱȣ®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º2011Äê°²»ÕÊ¡Öп¼ÊýѧģÄâÊÔ¾í£¨Ò»£©£¨½âÎö°æ£© ÌâÐÍ£º½â´ðÌâ

£¨´´ÐÂÌ⣩£®ÎÒÃÇʹÓõÄÈý½Ç°åÖÐÓÐ30°£¬45°£¬60°ºÍ90°ÌØÊâ½Ç£¬ÎÒÃǹ涨£ºÓÉÒ»¸±Èý½Ç°åÖеĽǼӣ¬¼õËùµÃµÄ½Ç³Æ֮Ϊ¡±°ëÌØÊâ½Ç¡±£®Èç135°=90°+45°µÈ£®ÈçͼÊÇÓÉÁ½¿éб±ßµÈ³¤µÄÈý½Ç°åÞÕ´Õ¶ø³ÉµÄ£¬
£¨1£©Ð´³öͼÖÐËùÓеÄСÓÚƽ½ÇµÄ¡±°ëÌØÊâ½Ç¡±ºÍËüÃǵĶÈÊý£»
£¨2£©ÀûÓÃͼÇósin15°µÄÖµ£»
£¨3£©½«Í¼Öк¬30°½ÇµÄÖ±½ÇÈý½Ç°åÑØAB·­Õ۵á÷ABC1£¬ÔÙ×÷¡÷ABC¹ØÓÚABÖеãOµÄÖÐÐĶԳơ÷ABC2£¬Á¬AC2£¬BC1£¬Ï߶ÎDC2£¬DC1·Ö±ð½»ABÓÚF£¬G£¬»­³öͼÐΣ¬Ö¸³öÆäÖеÄÁ½¶ÔÏàËÆÈý½ÇÐΣ¬²¢Çó³öÆäÖÐÒ»¶ÔÏàËÆÈý½ÇÐεÄÏàËƱȣ®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸