有弦长弓高怎么算半径 已知弦长和弓高求半径，怎么弄
\u8bf7\u95ee\u5df2\u77e5\u5706\u5f27\u7684\u5f13\u9ad8\u548c\u5f26\u957f\u6c42\u5706\u5f27\u534a\u5f84\uff0c\u90a3\u516c\u5f0f\uff1f\u8bbe\u5706\u5f27\u534a\u5f84\u4e3aR\uff0c\u5f13\u9ad8\u4e3ah\uff0c\u5f26\u957f\u4e3aL
\u5219\uff1aR²-(R-h)²=(L/2)²
R=h/2+L²/(8h)
\u6309\u4f60\u8ffd\u95ee\u7684\u6570\u636e\uff1aL=45\uff0ch=2\u4ee3\u5165
R=2/2+45²/(8*2)=127.5625
\u5173\u4e8e\u5706\u5f27\u7684\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b \uff1a
\uff081\uff09\u5706\u5f27\u7684\u5f27\u957f\uff1a \uff0c(R=\u534a\u5f84\uff0cn=\u5706\u5f27\u7684\u89d2\u5ea6\u7684\u7edd\u5bf9\u503c\uff09
\uff082\uff09\u6247\u5f62\u7684\u9762\u79ef\uff1a \uff0c(L=\u5706\u5f27\u7684\u5f27\u957f\uff0cR=\u534a\u5f84)
\u6269\u5c55\u8d44\u6599\uff1a
\u4efb\u610f\u4e00\u6761\u5706\u5f27\u53ef\u4ee5\u627e\u51fa\u5b83\u6240\u5728\u7684\u5706\u91cc\u7684\u5706\u5fc3\uff0c\u65b9\u6cd5\u5982\u4e0b\uff1a
\uff081\uff09\u9996\u5148\uff0c\u5728\u5706\u5f27\u4e0a\u4efb\u610f\u53d63\u70b9A\u3001C\u3001C\uff1b
\uff082\uff09\u8fde\u63a5AB/BC\u5f62\u6210\u4e24\u6761\u76f4\u7ebf\uff1b
\uff083\uff09\u7528\u5c3a\u5b50\u5206\u522b\u627e\u51faAB/BC\u4e24\u6761\u76f4\u7ebf\u7684\u4e2d\u70b9D/E\uff1b
\uff084\uff09\u5206\u522b\u4ee5D/E\u505aAB/BC\u7684\u5782\u76f4\u5e73\u5206\u7ebf\uff0c\u4e24\u6761\u5782\u76f4\u5e73\u5206\u7ebf\u4ea4\u4e0eF\u70b9\uff0c\u5219F\u70b9\u5c31\u662f\u5706\u5f27\u7684\u5706\u5fc3\u3002
\u5728\u5efa\u7b51\u5b89\u88c5\u5de5\u5730\u4e2d\uff0c\u7ecf\u5e38\u9047\u5230\u5706\u5f27\u653e\u7ebf\uff0c\u5982\u516c\u8def\u3001\u94c1\u8def\u3001\u6c34\u5229\u3001\u7535\u529b\u3001\u697c\u623f\u5efa\u7b51\u3001\u5e02\u653f\u56ed\u6797\u5de5\u7a0b\u4e2d\u7684\u5706\u5f62\u7ed3\u6784\u6216\u88c5\u9970\u7b49\uff0c\u51e0\u4e4e\u6709\u5efa\u7b51\u5efa\u8bbe\u7684\u5730\u65b9\u5c31\u6709\u5706\u5f27\u653e\u7ebf\u7684\u9700\u8981\u3002
\uff08\u534a\u5f84\uff09\u5e73\u65b9=\uff08\u5f26\u957f/2\uff09\u5e73\u65b9+\uff08\u534a\u5f84-\u5f13\u9ad8\uff09\u5e73\u65b9
\u5c06\u6570\u5e26\u8fdb\u53bb\u89e3\u65b9\u7a0b\u3002
如图，弦长为AB，弓高为CD，
设弓高CD=h，弦长的一半AD=a,半径为r,则在直角三角形AOD中，
AD^2+OD^2=OA^2, 即AD^2+(OC-CD)^2=OA^2
a^2+(r-h)^2=r^2,
整理，得，2hr=a^2+h^2,
r=(a^2+h^2)/2h
即，半径等于弦长一半与弓高的平方和除以弓高的2倍。
解如图。
如图所示：
因为这里书写不便，故将我的答案做成图像贴于下方，谨供楼主参考（若图像显示过小，点击图片可放大）。
绛旓細寮﹂暱L=1.65绫筹紝寮撻珮H=0.393绫筹紝姹傚崐寰R锛屾眰寮ч暱C 寮ф墍瀵圭殑鍦嗗績瑙掍负A銆俁^2=(R-H)^2+(L/2)^2 R^2=R^2-2*R*H+H^2+L^2/4 2*R*H=H^2+L^2/4 R=H/2+L^2/(8*H)=0.393/2+1.65^2/(8*0.393)=1.0624绫 A=2*ARC SIN((L/2)/R)=2*ARC SIN((3.42/2)/...
绛旓細(1)娴嬮噺鍑哄渾寮х殑寮﹂暱涓篖銆(2)鍦ㄥ鸡闀縇鐨1/2澶勶紙涓棿浣嶇疆锛夛紝娴嬮噺鍑哄渾寮х殑楂樹负H銆(3)鎸変笅寮忔潵璁＄畻鍑哄渾寮х殑鍗婂緞R锛歊=L^2/(8*H)+H/2 瀹冪敱涓嬪紡鎺ㄥ寰楀埌锛 R^2=(L/2)^2+(R-H)^2 鐢ㄥ紦寮︽硶娴嬮噺锛屽ぇ鐩村緞D,寮楂榟鍜屽鸡闀縎鐨勫叧绯绘槸 (D/2-h)^2+S^2/4=(D/2)^2 锛堢洿瑙...
绛旓細鍒╃敤鍕捐偂瀹氱悊锛屼篃灏辨槸浣犺繖绉嶇畻娉曪紝娌℃湁鍐嶇畝鍗曠殑浜 鍕捐偂瀹氱悊灏辨槸鍒濅腑瀛︾殑锛屽鏋滅洿瑙掍笁瑙掑舰涓ょ洿瑙掕竟鍒嗗埆涓篴锛宐锛屾枩杈逛负c锛岄偅涔坅² +b² =c² 锛 鍗崇洿瑙掍笁瑙掑舰涓ょ洿瑙掕竟鐨勫钩鏂瑰拰绛変簬鏂滆竟鐨勫钩鏂广傝繖灏辨槸鍕捐偂瀹氱悊锛屽涓鍒囩洿瑙掍笁瑙掑舰鎭掓垚绔嬨傚弽杩囨潵璇达細濡傛灉涓夎褰㈢殑涓夋潯杈筧锛宐锛宑婊¤冻a...
绛旓細鍥炵瓟锛歺*x+1.5*1.5=(1.8-x)(1.8-x) x=11/40=0.275 r=1.8-0.275=1.525. 娉ㄦ剰:寮︽墍瀵瑰姬鏄ぇ鍗婂渾鐨,涓嶆槸灏忓崐鍦嗐
绛旓細寮﹂暱L=4.2锛屽紦楂楬=0.8绫筹紝姹傚崐寰R锛屾眰寮ч暱C 寮ф墍瀵圭殑鍦嗗績瑙掍负A銆俁^2=(R-H)^2+(L/2)^2 R^2=R^2-2*R*H+H^2+L^2/4 2*R*H=H^2+L^2/4 R=H/2+L^2/(8*H)A=2*ARC SIN((L/2)/R)=2*ARC SIN C=PI*R*A/180 缁欎綘鍏紡寰閲岄潰甯﹀氨鍙互浜嗭紝涓汉鎰熻浣犺繖棰樻湁...
绛旓細杩鍗婂緞锛堝乏鎴栧彸涓鏉″崐寰勪互鍙婅繃寮撻珮鐨勪竴鏉★級銆傚洜涓哄紦楂樺钩鍒嗗鸡锛屽緱80/2=40 鍒檙^2=40^2+(r-32)^2 鍕捐偂瀹氱悊 銆俽=41
绛旓細寮ч暱C=16.088绫筹紝楂楬=2.5绫筹紝鍗婂緞R鏄灏?Rn+1=(1-(Rn*COS(C/(2*Rn))-Rn+H)/((C/2)*SIN(C/(2*Rn))-H))*Rn R0=12 R1=12.4643 R2=12.5006 R3=12.5008 R4=12.5008 R=12.5008绫
绛旓細R=46280,M楂32.3 瑙ｏ細琛ュ叏鍦,浣滆緟鍔╃嚎锛堝涓嬪浘锛変笁瑙掑舰OBC涓 OB^2+BC^2=OC^2 (R-80)^2+(620+2100)^2=R^2 R=46280 涓夎褰DM涓 OD^2+DM^2=OM^2 2100^2+DM^2=R^2 DM=46232.3(绾︼級MN=DM-(R-80)=32.3
绛旓細璁惧紦褰㈡墍鍦ㄦ墖褰㈢殑鍗婂緞涓篟锛屽垯鐢卞嬀鑲″畾鐞嗭紝(R-1.4)^2+(8.4/2)^2=R^2 瑙ｅ緱R=7 璁炬墖褰㈢殑灏栬涓篴锛屽垯sin(a/2)=(8.4/2)/R=3/5 鍒檃=2arcsin(3/5)鎵囧舰闈㈢Н=(1/2)aR^2=49arcsin(3/5)鈮49X(37/180)X蟺=31.64 涓夎褰㈤潰绉=(1/2)X8.4X(7-1.4)=23.52 寮撳舰闈㈢Н=鎵囧舰闈㈢Н...
绛旓細濡傚浘锛屾墍姹傞潰绉=0.70
