以知弧长拱高求半径
\u77e5\u9053\u5f27\u957f\u548c\u62f1\u9ad8\u600e\u4e48\u6c42\u534a\u5f84\u4ee4\u5f27\u957f\u4e3aL\uff0c\u62f1\u9ad8\u4e3ah\uff0c\u6c42\u534a\u5f84r
\u5047\u8bbe\u5f27\u957fL\u6240\u5939\u89d2\u4e3a\u03b8
\u5219\u6709L=2\u03c0r\u00d7\u03b8/360
\u8fc7\u5f27\u7684\u4e24\u4e2a\u7aef\u70b9\u505a\u5706\u5f27\u5207\u7ebf\u7684\u5782\u7ebf\uff0c\u4e0e\u5f27\u9ad8\u5ef6\u957f\u7ebf\u4ea4\u4e8e\u70b9O\uff0c\u70b9O\u5373\u4e3a\u5706\u5fc3\u3002
\u4e24\u6761\u5782\u7ebf\u6240\u5939\u89d2\u5373\u4e3a\u03b8\uff0c\u5f27\u7aef\u70b9\u81f3O\u7684\u8ddd\u79bb\u5373\u4e3ar\u3002
\u6839\u636e\u4f59\u5f26\u5b9a\u7406\uff0ccos(\u03b8/2)=(r-h)/r
\u7ed3\u5408\u4e24\u5f0f,\u03b8=180L/\uff08\u03c0r\uff09\uff0c\u5219\u03b8/2=90L/\uff08\u03c0r\uff09
cos\uff08\u03b8/2\uff09=1-h/r
cos[90L/(\u03c0r)]=1-h/r
\u8fd9\u662f\u5f27\u957f\u3001\u62f1\u9ad8\u548c\u534a\u5f84\u7684\u5173\u7cfb\u5f0f\u3002
n\u00b0\u7684\u5706\u5fc3\u89d2\u6240\u5bf9\u5f27\u957f\u4e3an\u03c0R/180\u00b0\uff0c\u5e7f\u4e49\u4e0a\u6307\u5149\u6ed1\u66f2\u7ebf\u7684\u5f27\u957f\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u62f1\u9ad8\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a\u8bbe\u534a\u5f84R\uff0c\u62f1\u5f62\u8ddd\u79bb\u4e3a2a\uff0c\u5219\u62f1\u9ad8h=R-\u221a(R²-a²)\u3002
\u5728\u9762\u5b9e\u4f53\u7684\u8fb9\u754c\u7ebf\u8ba1\u7b97\u4e2d\uff0c\u5728\u67d0\u70b9\u7684\u62f1\u9ad8\u6b63\u662f\u5bf9\u8fb9\u754c\u7ebf\u5728\u8be5\u70b9\u7684\u5f2f\u66f2\u7a0b\u5ea6\u548c\u51f8\u51f9\u6027\u7684\u53cd\u6620\uff0c\u8be5\u70b9\u7684\u4e2d\u5fc3\u8ddd\u79bb\u53c8\u53ef\u4ee5\u5bf9\u9762\u5b9e\u4f53\u5f62\u72b6\u7684\u6574\u4f53\u8fdb\u884c\u63cf\u8ff0\uff0c\u901a\u8fc7\u8fb9\u754c\u7ebf\u4e0a\u67d0\u70b9\u7684\u4e2d\u5fc3\u8ddd\u79bb\u548c\u62f1\u9ad8\u7ec4\u6210\u590d\u6570\uff0c\u5e76\u5bf9\u5176\u8fdb\u884c\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\u53ef\u4ee5\u83b7\u53d6\u5085\u91cc\u53f6\u5f62\u72b6\u63cf\u8ff0\uff0c\u4f5c\u4e3a\u5bf9\u9762\u5b9e\u4f53\u5f62\u72b6\u76f8\u4f3c\u5ea6\u7684\u5ea6\u91cf\u3002
\u5c06\u8fb9\u754c\u7ebf\u4e0a\u4efb\u4e00\u70b9pi\u6cbf\u8fb9\u754c\u7ebf\u987a\u65f6\u9488\u65b9\u5411\u548c\u9006\u65f6\u9488\u65b9\u5411\u5206\u522b\u626b\u63cf\u5f27\u957fl(ri/2)(l\u2208[0\uff0cL]\uff0cL\u4e3a\u8fb9\u754c\u7ebf\u5468\u957f)\uff0c\u5f97\u5230\u8fb9\u754c\u7ebf\u4e0a\u4e24\u70b9pi1\u548cpi2\uff0c\u5c06\u70b9pi\u5230\u7ebf\u6bb5pi1pi2\u7684\u8ddd\u79bb\u5b9a\u4e49\u4e3a\u8fb9\u754c\u7ebf\u5728\u8be5\u70b9\u7684\u62f1\u9ad8\uff0c\u8bb0\u4e3ahi\uff0c\u5176\u4e2dhi\u6ee1\u8db3\u4e0b\u9762\u6761\u4ef6\uff1a\u7ebf\u6bb5pi1pi2\u5728\u8fb9\u754c\u7ebf\u5185\u65f6hi>0\uff0c\u7ebf\u6bb5pi1pi2\u5728\u8fb9\u754c\u7ebf\u5916\u65f6h<0\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u5f27\u957f
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u62f1\u9ad8
\u6240\u6c42\u534a\u5f84\uff1a6164.81593961922
\u6240\u6c42\u89d2\u5ea6\uff1a46.46998391700668
\u6240\u6c42\u9762\u79ef\uff1a15412039.849048052
\u6240\u6c42\u5f26\u957f\uff1a4864.078921900514
答案如下图
根据弧度长求出这段弧的所对的圆心角，然后利用拱高，和圆心角的一半计算出半径
绛旓細cos[90L/(蟺r)]=1-h/r 杩欐槸寮ч暱銆佹嫳楂樺拰鍗婂緞鐨勫叧绯诲紡銆俷掳鐨勫渾蹇冭鎵瀵瑰姬闀夸负n蟺R/180掳锛屽箍涔変笂鎸囧厜婊戞洸绾跨殑寮ч暱銆
绛旓細鍥炵瓟锛氭暟瀛︿笂:宸茬煡寮ч暱L 銆鎷遍珮H,璁捐涓篴(寮у害)銆鍗婂緞r 鏈変袱涓柟绋嬪紡: L/2r= acosa=(r-H)/r 鍙槸杩欎釜鏂圭▼缁勮В璧锋潵姣旇緝楹荤儲
绛旓細寮ч暱l=鍗婂緞脳鍦嗗績瑙 鎷遍珮h=鍗婂緞-鍗婂緞脳cos(½鍦嗗績瑙)璁惧崐寰=r锛屽渾蹇冭=胃锛屽彲浠ュ缓绔嬪涓嬭仈绔嬫柟绋 r路胃=l 鈶 r[1-cos(½胃)]=h 鈶 鈭碵1-cos(½胃)]/胃=h/l 浠(胃)=[1-cos(½胃)]/胃-h/l鐢ㄤ簩鍒嗘硶鎴栬绠楄蒋浠舵眰闆剁偣锛屽彲姹傚嚭胃 浠ｅ洖鈶犲嵆鍙眰鍑哄崐寰勩
绛旓細寮ч暱鏄疌=725姣背,鎷遍珮鏄疕=130姣背,鍗婂緞搴旇鏄灏戯紵Rn+1=(1-(Rn*COS(C/(2*Rn))-Rn+H)/((C/2)*SIN(C/(2*Rn))-H))*Rn R0=505 R1=479.915 R2=482.017 R3=482.034 R4=482.034 R=482.034姣背
绛旓細濡傛灉鎷辨ˉ涓哄渾寮у舰鐨勮瘽锛屽彲璁捐法搴︿负2a锛屾嫳楂樹负h锛屽崐寰勪负R銆鍒橰^2=a^2+(R-h)^2锛屽彲寰楀崐寰凴=(a^2+h^2)/(2h)銆傚埄鐢ㄤ綑寮﹀畾鐞嗭紝閫氳繃鍗婂緞鍜岃法搴﹀彲浠ユ眰寰楁嫳妗ュ姬闀垮搴旂殑鍦嗗績瑙掞紝鐒跺悗鍗冲彲姹傚嚭寮ч暱銆
绛旓細鍗婂緞锛坮锛夊彲浠ラ氳繃鎷遍珮锛坔锛夊拰寮ч暱锛圕锛夋潵璁＄畻銆傚叕寮忎负锛歳 = h + C^2 / (8h)鍦ㄨ繖绉嶆儏鍐典笅锛屾垜浠凡鐭ユ嫳楂 h = 495锛屽姬闀 C = 2970銆傛墍浠ワ細r = 495 + 2970^2 / (8 * 495)r = 495 + (2970^2) / 3960 r = 495 + (887,900) / 3960 r = 495 + 225.55 r = 720.55 鎵...
绛旓細鍥犱负杩欓噷涔﹀啓涓嶄究锛屾晠灏嗘垜鐨勭瓟妗堝仛鎴愬浘鍍忚创浜庝笅鏂癸紝璋ㄤ緵妤间富鍙傝冿紙鑻ュ浘鍍忔樉绀鸿繃灏忥紝鐐瑰嚮鍥剧墖鍙斁澶э級
绛旓細琛ュ厖锛 銆 鎴戝仛鍑烘潵浜嗭紝淇濊瘉娌￠敊锛岃璁ょ湡鐐瑰埆娴垂鎴戠殑鑴戝姏 銆 鍙栨嫳绔偣涓鎷遍珮杩炴帴绾挎锛岄噺鍑烘嫳楂樹笌璇ョ嚎娈佃鐨勫害鏁帮紝璁颁笅鏉ワ紝鍐嶄粠鎷辩鐐瑰仛涓鏉″皠绾匡紝璇ュ皠绾夸笌绾挎鐨勮搴︿笌鎷遍珮涓庤绾挎瑙掔殑搴︽暟涓鏍凤紝寤堕暱鎷遍珮绾挎鎴愮洿绾夸笌灏勭嚎鐩镐氦锛屾垚涓ょ嚎娈碉紝闅忓彇涓鏉＄嚎娈靛氨鏄鍗婂緞銆愪竴鏉″皠绾跨嚎娈碉紝涓鏉″欢闀挎嫳楂樼殑鐩...
绛旓細鐢寮ч暱鍏紡寰楀埌鍦嗗績瑙掑拰鍗婂緞鐨勫叧绯伙紝鍐嶆眰鍑哄鸡闀匡紝鍒╃敤鍕捐偂瀹氱悊姹傚嚭鍗婂緞
绛旓細璁惧渾蹇冭涓何革紝鍗婂緞涓簉.宸茬煡寮ч暱涓簂锛鎷遍珮h.鍒欐湁锛宺路胃=l,cos胃/2=锛坮-h锛/r 姹傝В鏂圭▼缁勶紝鍙互瑙ｅ緱r.杩欓噷鍙槸鎻愪緵浜嗘柟娉曪紝鍓╀笅閮ㄥ垎璇疯嚜琛岃В绛斻
