ÌâÄ¿ÄÚÈÝ
ÔÚÒ»¸öÌض¨Ê±¶ÎÄÚ£¬ÒÔµãEΪÖÐÐĵÄ7º£ÀïÒÔÄÚº£Óò±»ÉèΪ¾¯½äË®Óò£®µãEÕý±±55º£Àï´¦ÓÐÒ»¸öÀ×´ï¹Û²âÕ¾A£®Ä³Ê±¿Ì²âµÃÒ»ËÒÔÈËÙÖ±ÏßÐÐÊ»µÄ´¬Ö»Î»ÓÚµãA±±Æ«¶«45¡ãÇÒÓëµãAÏà¾à402 |
| ||
26 |
13 |
£¨I£©Çó¸Ã´¬µÄÐÐÊ»Ëٶȣ¨µ¥Î»£ºº£Àï/Сʱ£©£»
£¨II£©Èô¸Ã´¬²»¸Ä±äº½Ðз½Ïò¼ÌÐøÐÐÊ»£®ÅжÏËüÊÇ·ñ»á½øÈ뾯½äË®Óò£¬²¢ËµÃ÷ÀíÓÉ£®
·ÖÎö£º£¨1£©Ïȸù¾ÝÌâÒ⻳ö¼òͼȷ¶¨AB¡¢AC¡¢¡ÏBACµÄÖµ£¬¸ù¾Ýsin¦È=
Çó³ö¦ÈµÄÓàÏÒÖµ£¬ÔÙÓÉÓàÏÒ¶¨ÀíÇó³öBCµÄÖµ£¬´Ó¶ø¿ÉµÃµ½´¬µÄÐÐÊ»Ëٶȣ®
£¨2£©ÏȼÙÉèÖ±ÏßAEÓëBCµÄÑÓ³¤ÏßÏཻÓÚµãQ£¬¸ù¾ÝÓàÏÒ¶¨ÀíÇó³öcos¡ÏABCµÄÖµ£¬½ø¶ø¿ÉµÃµ½sin¡ÏABCµÄÖµ£¬ÔÙÓÉÕýÏÒ¶¨Àí¿ÉµÃAQµÄ³¤¶È£¬´Ó¶ø¿ÉÈ·¶¨QÔÚµãAºÍµãEÖ®¼ä£¬¸ù¾ÝQE=AE-AQÇó³öQEµÄ³¤¶È£¬È»ºó¹ýµãE×÷EP¡ÍBCÓÚµãP£¬ÔòEPΪµãEµ½Ö±ÏßBCµÄ¾àÀ룬½ø¶øÔÚRt¡÷QPEÖÐÇó³öPEµÄÖµÔÚÓÚ7½øÐбȽϼ´¿ÉµÃµ½´ð°¸£®
| ||
26 |
£¨2£©ÏȼÙÉèÖ±ÏßAEÓëBCµÄÑÓ³¤ÏßÏཻÓÚµãQ£¬¸ù¾ÝÓàÏÒ¶¨ÀíÇó³öcos¡ÏABCµÄÖµ£¬½ø¶ø¿ÉµÃµ½sin¡ÏABCµÄÖµ£¬ÔÙÓÉÕýÏÒ¶¨Àí¿ÉµÃAQµÄ³¤¶È£¬´Ó¶ø¿ÉÈ·¶¨QÔÚµãAºÍµãEÖ®¼ä£¬¸ù¾ÝQE=AE-AQÇó³öQEµÄ³¤¶È£¬È»ºó¹ýµãE×÷EP¡ÍBCÓÚµãP£¬ÔòEPΪµãEµ½Ö±ÏßBCµÄ¾àÀ룬½ø¶øÔÚRt¡÷QPEÖÐÇó³öPEµÄÖµÔÚÓÚ7½øÐбȽϼ´¿ÉµÃµ½´ð°¸£®
½â´ð£º½â£º£¨I£©Èçͼ£¬AB=40
£¬AC=10
£¬¡ÏBAC=¦È£¬sin¦È=
£®
ÓÉÓÚ0¡ã£¼¦È£¼90¡ã£¬ËùÒÔcos¦È=
=
£®
ÓÉÓàÏÒ¶¨ÀíµÃBC=
=10
£®
ËùÒÔ´¬µÄÐÐÊ»ËÙ¶ÈΪ
=15
£¨º£Àï/Сʱ£©£®
£¨II£©ÈçͼËùʾ£¬ÉèÖ±ÏßAEÓëBCµÄÑÓ³¤ÏßÏཻÓÚµãQ£®
ÔÚ¡÷ABCÖУ¬ÓÉÓàÏÒ¶¨ÀíµÃ£¬
cos¡ÏABC=
=
=
£®
´Ó¶øsin¡ÏABC=
=
=
£®
ÔÚ¡÷ABQÖУ¬ÓÉÕýÏÒ¶¨ÀíµÃ£¬
AQ=
=
=40£®
ÓÉÓÚAE=55£¾40=AQ£¬ËùÒÔµãQλÓÚµãAºÍµãEÖ®¼ä£¬ÇÒQE=AE-AQ=15£®
¹ýµãE×÷EP¡ÍBCÓÚµãP£¬ÔòEPΪµãEµ½Ö±ÏßBCµÄ¾àÀ룮
ÔÚRt¡÷QPEÖУ¬PE=QE•sin¡ÏPQE=QE•sin¡ÏAQC=QE•sin£¨45¡ã-¡ÏABC£©
=15¡Á
=3
£¼7£®
ËùÒÔ´¬»á½øÈ뾯½äË®Óò£®
2 |
13 |
| ||
26 |
ÓÉÓÚ0¡ã£¼¦È£¼90¡ã£¬ËùÒÔcos¦È=
1-(
|
5
| ||
26 |
ÓÉÓàÏÒ¶¨ÀíµÃBC=
AB2+AC2-2AB•AC•cos¦È |
5 |
ËùÒÔ´¬µÄÐÐÊ»ËÙ¶ÈΪ
10
| ||
|
5 |
£¨II£©ÈçͼËùʾ£¬ÉèÖ±ÏßAEÓëBCµÄÑÓ³¤ÏßÏཻÓÚµãQ£®
ÔÚ¡÷ABCÖУ¬ÓÉÓàÏÒ¶¨ÀíµÃ£¬
cos¡ÏABC=
AB2+BC2-AC2 |
2AB•BC |
402¡Á2+102¡Á5-102¡Á13 | ||||
2¡Á40
|
3
| ||
10 |
´Ó¶øsin¡ÏABC=
1-cos2¡ÏABC |
1-
|
| ||
10 |
ÔÚ¡÷ABQÖУ¬ÓÉÕýÏÒ¶¨ÀíµÃ£¬
AQ=
ABsin¡ÏABC |
sin(45¡ã-¡ÏABC) |
40
| ||||||||
|
ÓÉÓÚAE=55£¾40=AQ£¬ËùÒÔµãQλÓÚµãAºÍµãEÖ®¼ä£¬ÇÒQE=AE-AQ=15£®
¹ýµãE×÷EP¡ÍBCÓÚµãP£¬ÔòEPΪµãEµ½Ö±ÏßBCµÄ¾àÀ룮
ÔÚRt¡÷QPEÖУ¬PE=QE•sin¡ÏPQE=QE•sin¡ÏAQC=QE•sin£¨45¡ã-¡ÏABC£©
=15¡Á
| ||
5 |
5 |
ËùÒÔ´¬»á½øÈ뾯½äË®Óò£®
µãÆÀ£º±¾ÌâÖ÷Òª¿¼²éÕýÏÒ¶¨Àí¡¢ÓàÏÒ¶¨ÀíµÄÓ¦Ó㮿¼²éѧÉúµÄÔËËãÄÜÁ¦¡¢×ۺϿ¼ÂÇÎÊÌâµÄÄÜÁ¦£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿