半径为1的球面上有三点A，B，C，若A和B，A和C，B和C的球面距离都是 π 2 ，过A、B、C三点做截
\u5df2\u77e5A\u3001B\u3001C\u662f\u534a\u5f84\u4e3a1\u7684\u7403\u9762\u4e0a\u4e09\u70b9\uff0cO\u4e3a\u7403\u5fc3\uff0cA\u3001B\u548cA\u3001C\u7684\u7403\u9762\u8ddd\u79bb\u90fd\u662f\u03c0/2\uff0cB\u3001C\u7684\u7403\u9762\u8ddd\u79bb\u662f\u03c0/3
\u7403\u534a\u5f84R=1
\u89d2AOB=\u03c0/2,AB=2sin(\u03c0/4)=\u6839\u53f72,AC=AB=\u6839\u53f72
\u89d2BOC=\u03c0/3,BC=2sin(\u03c0/6)=1
sin(\u89d2BAC/2)=(1/2)/(\u6839\u53f72)=1/(2(\u6839\u53f72))=(\u6839\u53f72)/4
cos(\u89d2BAC/2)=(1-((\u6839\u53f72)/4)^2)^(1/2)=(1/4)(\u6839\u53f7(14)
sin(\u89d2BAC)=2sin(\u89d2BAC/2)cos(\u89d2BAC/2)=(1/4)(\u6839\u53f77)
\u8bbe\u4e09\u89d2\u5f62ABC\u7684\u5916\u63a5\u5706\u534a\u5f84=r
2r=BC/sin(\u89d2BAC)=4/(\u6839\u53f77)
r=2/(\u6839\u53f77)
\u7403\u5fc3O\u5230\u5e73\u9762ABC\u7684\u8ddd\u79bb=(R^2-r^2)^(1/2)=(1-(4/7))^(1/2)=(1/7)(\u6839\u53f721)
A\u548cC\u7684\u7403\u9762\u8ddd\u79bb\u90fd\u662f\u03c0\uff0f2\uff0c 2\u03c0r\u00f7\u03c0/2=4 \u6240\u4ee5A\u4e0eC\u5bf9\u5e94\u7684\u5706\u5fc3\u89d2\u662f360\u00b0\u00f74=90\u00b0\uff0c\u540c\u6837\u7684\u9053\u7406\uff0cA\u4e0eB\u5bf9\u5e94\u7684\u5706\u5fc3\u89d2\u4e5f\u662f360\u00b0\u00f74=90\u00b0\uff0c\u4ee5\u5706\u5fc3O\u4e3a\u539f\u70b9\u5efa\u7acb\u7a7a\u95f4\u76f4\u89d2\u5750\u6807\u7cfb\uff0c\u5e76\u4ee4A=(1,0,0), B=(0,1,0),\u56e0\u4e3aB\u548cC\u7684\u7403\u9762\u8ddd\u79bb\u662f\u03c0\uff0f3. B\u4e0eC\u5bf9\u5e94\u7684\u5706\u5fc3\u89d2\u662f360\u00b0\u00f76=60\u00b0 \u6240\u4ee5C=(0,1/2\uff0c2\u5206\u4e4b\u6839\u53f73)\uff0cA\u3001B\u3001C\u7684\u5750\u6807\u90fd\u51fa\u6765\u4e86\uff0c\u95ee\u9898\u81ea\u5df1\u89e3\u51b3\u597d\u4e0d\u597d\uff01\u795d\u4f60\u8003\u8bd5\u6109\u5feb\u54c8\uff01
球心O与A，B，C三点构成正三棱锥O-ABC，
已知OA=OB=OC=R=1，∠AOB=∠BOC=∠AOC=90°，
由此可得AO⊥面BOC．
∵ S △BOC = ， S △ABC =
鍗婂緞涓1鐨勭悆闈笂鏈変笁鐐笰銆丅銆丆,鍏朵腑AB=1,BC=鈭3,A銆丆涓ょ偣闂寸殑鐞冮潰璺...
绛旓細瑙ｏ細鈭电悆O鐨鍗婂緞涓1锛孉銆丆涓ょ偣闂鐨勭悆闈璺濈涓合2锛屸埓鈭燗OC=蟺2 鈭碅C=鈭2 鈭礎B=1锛孊C=鈭3锛鈭粹垹BAC=蟺2 鈭寸悆蹇冨湪骞抽潰ABC鍐呯殑灏勫奖涓築C鐨勪腑鐐 鈭寸悆蹇冨埌骞抽潰ABC鐨勮窛绂讳负鈭1-(鈭32)2=12 鏁呴塀锛
鍗婂緞涓1鐨勭悆闈笂鏈変笁鐐笰,B,C,鑻鍜孊,A鍜孋,B鍜孋鐨勭悆闈㈣窛绂婚兘鏄 蟺 2...
绛旓細鐞冨績O涓A锛孊锛C涓夌偣鏋勬垚姝ｄ笁妫遍敟O-ABC锛屽凡鐭A=OB=OC=R=1锛屸垹AOB=鈭燘OC=鈭燗OC=90掳锛岀敱姝ゅ彲寰桝O鈯ラ潰BOC锛庘埖 S 鈻矪OC = 1 2 锛 S 鈻矨BC = 3 2 锛庤鐞冨績鍒伴潰鐨勮窛绂讳负h锛岀敱V A-BOC =V O-ABC 锛屽緱 h= 3 3 锛庢墍浠ョ悆蹇僌 鍒板钩闈BC...
鍗婂緞涓1鐨勭悆闈笂鏈堿銆丅銆丆涓夌偣,鍏朵腑鐐笰涓嶣銆丆涓ょ偣闂寸殑鐞冮潰璺濈鍧囦负蟺2...
绛旓細瑙ｏ細鐞冨績O涓A锛孊锛C涓夌偣鏋勬垚涓夋１閿-ABC锛屽鍥炬墍绀猴紝宸茬煡OA=OB=OC=R=1锛屸垹AOB=鈭燗OC=90掳锛屸垹BOC=60掳锛岀敱姝ゅ彲寰桝O鈯ラ潰BOC锛庘埖S鈻矪OC锛12脳32锛庘埓鐢盫O-ABC=VA-BOC=13脳34脳1=312锛庢晠绛旀涓猴細312锛
鍗婂緞涓1鐨勭悆闈笂鏈堿,B,C涓夌偣,鍏朵腑A鍜孊鐨勭悆闈㈣窛绂,A鍜孋鐨勭悆闈㈣窛绂婚兘鏄...
绛旓細锛1锛夌敱棰樻剰鐭ワ細鈭燗OC=蟺2锛屸垹AOB=蟺2锛屸垹BOC=蟺3锛屸埓AO鈯ラ潰BOC鈭礝A=OB=OC=1锛屸埓AB=AC=2锛孊C=1锛庘埖VA?OBC锛13S鈻砄BC|AO|锛312鍙圴A?OBC锛13S鈻矨BC?h锛坔涓篛鍒板钩闈BC鐨勮窛绂伙級鈭礢鈻矨BC锛74鈭磆锛217鈭寸悆蹇僌鍒板钩闈BC鐨勮窛绂217锛4鍒嗭級锛2锛夎繃O浣淥D鈯C锛屸埖AO鈯ラ潰BOC锛屼笖OD?闈...
鍗婂緞涓1鐨勭悆闈笂鏈 涓夌偣,鍏朵腑鐐 涓 涓ょ偣闂寸殑鐞冮潰璺濈鍧囦负 , 涓ょ偣闂寸殑...
绛旓細B 璇曢鍒嗘瀽锛氭牴鎹鎰忓彲鐭ワ細鐞冨績O涓A锛孊锛C涓夌偣鏋勬垚涓夋１閿-ABC锛屼笖OA=OB=OC=R=1锛屸垹AOB=鈭燗OC=90掳锛屸垹BOC=60掳锛屾晠AO鈯ラ潰BOC锛庢墍浠ユ棰樺彲浠ユ牴鎹綋绉硶姹傚緱鐞冨績O鍒板钩闈BC鐨勮窛绂. 瑙ｏ細鐞冨績O涓嶢锛孊锛孋涓夌偣鏋勬垚涓夋１閿-ABC锛屽鍥炬墍绀猴紝 宸茬煡OA=OB=OC=R=1锛屸垹AOB=鈭燗OC=90掳...
A,B,C鏄鍗婂緞涓1鐨勭悆闈笂鐨涓夌偣
绛旓細璁綩(0,0,0),A(0,0,1),B(1,0,0),C(1/2,sqrt(3)/2,0)V(O-ABC)=1/3*1*sqrt(3)/4=sqrt(3)/12 S(ABC)=1/2|ABxAC| =1/2|(sqrt(3)/2,,1/2,sqrt(3)/2)| =7/8 d=(sqrt(3)/4)/(7/8)=2sqrt(3)/7 ...
璁続銆丅銆丆鏄鍗婂緞涓1鐨勭悆闈笂鐨涓夌偣,B銆丆涓ょ偣闂寸殑鐞冮潰璺濈涓合3,鐐笰涓...
绛旓細瑙ｏ細濡傚浘锛岋紙1锛夊洜涓虹悆O鐨鍗婂緞涓1锛孊銆丆涓ょ偣闂鐨勭悆闈璺濈涓合3锛岀偣A涓嶣銆丆涓ょ偣闂寸殑鐞冮潰璺濈鍧囦负蟺2锛屾墍浠モ垹BOC=蟺3锛屸垹AOB=鈭燗OC=蟺2锛庯紙2锛夊洜涓築C=1锛孉C=AB=2锛屾墍浠ョ敱浣欏鸡瀹氱悊寰梒os鈭燘AC=34锛宻in鈭燘AC=74锛岃鎴潰鍦嗙殑鍦嗗績涓篛1锛岃繛鎺O1锛屽垯鎴潰鍦嗙殑鍗婂緞R=AO1锛岀敱姝ｅ鸡瀹氱悊寰梤=BC2...
鍗婂緞涓1鐨勭悆闈笂鏈堿,B,C涓夌偣,鍏朵腑A鍜孊鐨勭悆闈㈣窛绂,A鍜孋鐨勭悆闈㈣窛绂婚兘鏄/...
绛旓細A涓嶣瀵瑰簲鐨勫渾蹇冭涔熸槸360掳梅4=90掳锛屼互鍦嗗績O涓哄師鐐瑰缓绔嬬┖闂寸洿瑙掑潗鏍囩郴锛屽苟浠=(1,0,0), B=(0,1,0),鍥犱负B鍜孋鐨勭悆闈璺濈鏄锛3. B涓嶤瀵瑰簲鐨勫渾蹇冭鏄360掳梅6=60掳 鎵浠=(0,1/2锛2鍒嗕箣鏍瑰彿3)锛孉銆丅銆丆鐨勫潗鏍囬兘鍑烘潵浜嗭紝闂鑷繁瑙ｅ喅濂戒笉濂斤紒绁濅綘鑰冭瘯鎰夊揩鍝堬紒
宸茬煡鍗婂緞涓1鐨勭悆闈笂鏈堿.B.C涓変釜鐐,涓斿畠浠箣闂寸殑鐞冮潰璺濈閮戒负3鍒嗕箣娲...
绛旓細鍏堟眰鍑哄鸡闀涓1锛60搴﹀渾蹇冭鍗婂緞绛変簬寮﹂暱锛孉B=AC=BC=1锛屽湪绛夎竟涓夎褰BC涓叾楂樹负鈭3/2锛屽唴蹇冧笌椤剁偣璺濈涓衡垰3/3锛鐞冨績O鍒板钩闈BC鐨勮窛绂=鈭1^2-(鈭3/3)^2=鈭6/3.
鍗婂緞涓1鐨勭悆闈笂鏈堿銆丅銆丆 涓夌偣, A 涓嶣銆丄 涓嶤 涔嬮棿鐨勭悆闈㈣窛绂婚兘鏄/...
绛旓細姹侽鐐瑰埌骞抽潰ABC鐨勮窛绂汇傜敱浜庘垹BOC=60掳涓擝O=CO锛屾墍浠D锛圖涓築C鐨勪腑鐐癸級鍨傜洿BC锛屼笖OD=鈭3/2锛涢氳繃璇佹槑鍙煡AO鍨傜洿骞抽潰BCO锛屽嵆AO鍨傜洿BC锛屼笖OD鍨傜洿BC锛屼粠鑰岃瘉鏄嶣C鍨傜洿骞抽潰AOD锛屽嵆骞抽潰AOD鍨傜洿骞抽潰ABC锛岃绠桝D=鈭7/2锛涗粠鑰屽緱鍑篛鐐瑰埌ABC骞抽潰鐨勮窛绂=1*锛堚垰3/2锛/锛堚垰7/2锛=鈭氾紙3/7锛
扩展阅读：45度pvc弯头对照表 ...
tan三角函数值 ...
大0.51进一球怎么算 ...
1比0.5的坡示意图 ...
提成0.5%是多少钱 ...
1.999倍的平台 ...
客队0+0.5是什么意思 ...
小0.51球是怎么算的 ...
半径为r的球面的gauss ...
| | |
